What's the weak link in my system?

Well maybe what you are hearing is that vinyl is a challenged medium. Noise, distortion and dynamic range are all far less than what real music needs, or than what digital sources can deliver. Hence a muddled sound.
Marantz cd players are excellent, so if the sound is still harsh, it is either your expectation that is wrong (real music can sound rather harsh), or the speakers, or the hard acoustics of the listening room.
In any system the weakest links are not modern electronics, but the speakers and the room. If it is the speakers, try auditioning Harbeths. They excell at avoiding listening fatigue.

The subjective magic of vinyl is that it compresses the dynamics. So the softer sounds are lifted a bit, and this gives an impression of more detail, but it is at the expense of more realistic dynamics. Add a hefty dose of harmonic distortion that many find euphonic, and you have most of what the attraction of vinyl is about. Remember, the vinyl sound can be emulated to perfection in the digital domain (studio mastering systems have such plug ins). So it is a deviation of the neutrality. It is also a money maker for small industries. Of course, you are perfectly free to enjoy this candle light view of the world.
I am of a generation when there was only vinyl, and I still own one of the famous vinyl systems of the day. I love the mechanical beauty of the SME arm, and I even sometimes enjoy the ritual, but for purely audio quality it is easily beaten by even a modest CD/BD player or a Chromecast Audio.

As for speaker placement and room modes, the simplest way to procede is to use REW (room equalization wizard, a free software package, see here: https://www.roomeqwizard.com/) and a cheap calibrated microphone to measure in room response. I am sure you will be horrified. Next, move the speakers around and add some rugs etc, as per advice here, to see if you can improve the response. If you want to improve the response more, you will need to use a parametric equalizer, either in software or in hardware. See here for a software one: https://sourceforge.net/projects/equalizerapo/

Sure, if you want good audio you have to say goodbuy to the vinyl romance anyway.  However, if you really want to hang on to your vinyl setup, you can also do the equalization in hardware.

As I teach my students, the truthfulness of a statement does not depend on who is making it, (let alone on the content of their living room). However, I don’t mind. I have two serious systems:
1 main system in the large living room
Speakers: Quad ESL 2805 (at full range), with B&W PV1d subwoofer and Antimode 8033 room eq. Crossover at 33 Hz, and 4th order slope.
Amplifier: Quad 33/606-2 (both refurbished, of course). The pre amp had its input senstivities modified to match modern sources (this is very important).
Sources: a modest Panasonic BD player, a Panasonic Plasma TV, a Chromecast Audio.
Souces still connected but no longer used: Linn Sondek/SME/Shure V15iii turntable, and Quad FM3 tuner (I now use internet radio for its superior sound quality).
And for those of you who are interested in cables: ordinary heavy duty speaker cable and quality interconnects with Nakamichi connectors, put together by a pro audio engineer.
Upgrade plans include firstly a second sub for even smoother response, and perhaps a DSpeaker X4 pre amp for improved room eq and its inbuilt DAC (but maybe it will be an Oppo 205). The Quad 33 is getting a bit long in the tooth.

Secundary system in my 18 sq m study
Harbeth P3ESR as desktop speakers, raised to get the tweeter exactly at ear height (crucial for all dynamic speakers, and often overlooked).
Amplifier: Quad 405-2 (refurbished of course), input senstivity lowered by inline attenuators.
Volume control: Emotiva Control Freak
Source, desktop PC, with external ODAC usb dac.
Because the speakers still had a slight bass boost as a result of the proximity to the desk surface I equalized them a bit with the equalizer APO.

So as you can see I live by my conviction. Also, I am not one prone to the upgrade virus. My first system was QUAD esl57 with the 33/303 and that Linn SME combo and that was in the mid seventies. I later added a Philips cd player, subsequently replaced by a Marantz unit when we wanted a DVD player and similarly now the BD player. If and when there will be enough UHD video content, I will probably replace that with an Oppo 205 (perhaps also used as a pre amp). For years, the system in my study used the Rogers LS3/5a monitor, until I replaced it by the far better Harbeth P3ESR.
I do like having my tv screen attached to the stereo. I am not a home video buff, but I like better sound when I watch tv, and I think the video is an important part of the recorded opera/ballet experience. A good example is the magnificent Gergiev recording of the Ballets Russes at the Mariinski theater.

Geoff, sorry about the spelling mistake - English is not my native language.

Dave, you made a philosophical mistake that is taught in undergraduate class. That is all I said.
Beyond that, I knew you would play the heads I win, tails you loose game. Still, that does not mean you are right. I know I will never convince you because science and the scientific method are irrelevant in your phantasy world, but here is a proper test of the Chromecast Audio: http://archimago.blogspot.nl/2016/02/measurements-google-chromecast-audio_27.html
As it so happens, I also listen to real live (acoustical) music, and I must say that on the main system the recorded version (if recorded well) comes pretty close, apart from the inevitably more limited dynamic range compared to a live symphony orchestra or choir. But then, we don't live in concert halls or churches.
Not sure what you mean by the piece of glass, but go and listen to a live classical concert, and you will discover that there is not that much soundstage and imaging going on either when you close your eyes.

Dave,
Your argument is valid if more expensive sources made a difference, but not if they don’t. I am not quite sure where the minimum is exactly, and it may be wise to pay a bit extra to be on the safe side, but sonically perfect sources do not have to cost an arm and a leg anymore. See here for the specs of my usb DAC: https://www.jdslabs.com/products/39/odac-objectivedac/ Those are well beyond the hearing acuity of any human. That is the great benefit of technical progress. Perfection can be defined in relation to that human hearing acuity. There is no possible audible advance beyond that perfection, but such perfection is getting cheaper, and we are there. I admit to a kind of naughty pleasure in referring to the ultracheap Chromecast Audio, but it is indeed the best example of the progress we made, even if it does not measure perfectly (but almost). The good news is that at least for this part of the chain perfect audio is now within reach of all social classes, and not just to those who want to brag about their wealth. So to continue the bragging, they have to invent their alternative facts. I for one will not waste money on the advice of some spoonbenders, against the advice of the designer of my speakers, and against the advice of the designer of the original cd format. Did you actually read the Chromecast Audio test, or any of the other tests on that site? Is anything wrong with the test?
As for the plasma screen, my Quad speakers are dipoles so do not radiate sound to their sides. How else can you watch opera or ballet (or don’t you?). My experiences with live acoustic music do matter (and yes, I did sit in e.g. the Mariinski in St Petersburg) because they provide a yardstick.
There is one thing I forgot to mention about my system, and that is the house itself. It is a detached home in a quiet leafy suburb, and that is important, because detail resolution is obviously greatly impaired by background noise. So when it was designed we set about making sure it was as quiet as possible. Construction is concrete (also for the roof) and brick, and the heating and water piping system were designed to be as quiet as possible (no air heating or air conditioning, which we do not need/use here anyway). The same applies to our modern ultra quiet kitchen appliences. Ventilation openings to the outside are muffled, and the window glazing is specially sound deadening. These are cheap things to do when you build a house, but obviously hard to achieve afterwards. But they make a real sonic difference, comparable to listening in the middle of the night. Money much better spent than on cables or other quack stuff.

Guru's are, of course, just that.

i.e. frauds.