Replace vintage NAD 7020?

I’m wondering about the best inexpensive way to upgrade my barebones and mostly vintage system. All advice greatly appreciated, as I am a real novice! I bought this budget audiophile system back in the early 80s: NAD 7020 receiver (same amp as the 3020), Dual 505-2 TT and Snell Es. A vinyl fan, I held out on getting a decent CD player until 5 yrs ago, when I purchased a Consonance Linear 120. At the moment I live in a city apartment, so most of my listening is through Sennheiser HD_250 Linear II headphones. I listen almost exclusively to classical music, esp string quartets.

I’ve been satisfied with this system, given my budget, and it has held up well over the years. But my impression is that audio QPR has improved a lot and wonder if I can start to move toward something nicer. My main concern is that the sound seems too “laid back”, and lacking transparency and detail. While I prefer this to something with an overly bright midrange or treble (I bought the Consonance player because of its slightly warm and “analogue” sound), I wonder if it’s time to replace the NAD. I can only afford ~$600-800 to upgrade, though. Would a newer SS integrated amp like a used Arcam, say, make much of an impact? I read conflicting things about how important the amp is to the overall sound, and some people seem to think very highly of the NAD 3020 even now. So is it the right place to put the $$? If so, should I look for an amp with a phono stage or go with separates (e.g. a used Cambridge Audio integrated and 640P phono stage, presuming that matching amp to phono stage matters)? If not, is the alternative just to save the $$ and think about new speakers when I have a place I’ll be able to listen to them again (which should be fairly soon). Many thanks in advance.
I owned Snell E-III's and I will say they were a completely different sounding spk. when I introduced a powerful amp in the system (Bryston 4B-ST)! I presently own a little NAD 302 which is similiar in power to your 7020. This is a GREAT sounding little amp but I hear it's limitations. If you are handy w/a soldering iron and want to upgrade what you have, I'd start w/new spk. binding posts. But, it may be that your receiver may need new capacitors and other parts which may making replacing not worthy esp, if you're paying someone to do the work. I'm thinking you may want to sell your 7020 and get a newer NAD int. amp (326 BEE) because you said there isn't enough detail and resolution in your system. As far as a phone stage, I own a Creek 8SE and it is excellent sounding and compact. Please, I never owned a 7020, so it may be the greatest. BUT, it still a receiver and asked to do all in one package. Good Luck!
Until you select tuner, the 7020 is essentially the same as the 3020 int amp. I have had a couple of 3020s, one was my first amp, and I wish I still had one. Many have high regard for the preamp section of the 20 series, and you might try it with a separate power amp. This could be a stepping stone to separates if you can get a preamp in the future.
Just a suggestion for another way to might go.
upgrade nothing.
my parents have the 7020 along with B&W DM23 speakers, I am always struck by the musical qualities this combo has. Very listenable and tuneful though it is lacking a bit in detail and a bit thick.

I recently hooked up my 3020 and saw a spark near the power supply (I think it was the power supply, in the rear left) and it started to hum so i bought a 325 and it has many of the same qualities, a bit warm and thick but wonderfully musical and nicely detailed.

fwiw I agree on keeping the 7020 but if you feel the need to upgrade and like the house sound you may want to buy one of their newer amps.

you could also upgrade/swap cables
Grab any NAD from the late 80s or early 90s (3225PE, 7225PE, etc), and they're wonderful sounding. I still love and use my 7225PE I bought new in 1991 when I was a junior in high school, and it sounds damn fine w/anything from NIN to Mozart.
Thanks for all the responses. Kotta, not sure if the issue is lack of power, as I believe the original Es are a bit more efficient than the E-iiis. Could be wrong about this, but in any case I also experience via headphones the "thickness" -- a good way to describe it-- and lack of detail/transparency. Philjolet, I actually auditioned B&W DM23s way back when I was buying the speakers to go w/ the NAD. Maybe your parents and I went to the same dealer:) I think I chose the Snells partly because of greater efficiency, btw.

Anyway, I guess I will hold off for now and use the $$ for something less important like my son's education:)

And I'll look into new ICs, as the ones I have are el cheapo. Never seriously auditioned any but I guess worth a try.