Need some Amp help - a little new to properly powering speakers

I don't know of any proper test of the Yamaha, but it may well be pretty good (and not mid-fi) if it compares to e.g. the Yamaha AS700 tested here: http://i.nextmedia.com.au/Assets/Yamaha_AS-700_Amplifier_Review_LoRes.pdf
The need for power largely depends on the music you play, the size of the room and the sensitivity of the speakers (88dB in this case). Unless the room is very large 150 watt per channel should be OK, even if (up to a point) more is always better (for cleaner response to dynamic peaks). More amplifier power does not need to cost much, of course. Better speakers would make a bigger difference, but will cost significantly more.

FWIW, Polk in general are looked down upon by audiophiles with some good reasoning. Vintage Polk not so much as they were much more suited for the audiophile world. Polk headed in a downward spiral after they courted the mass market and nothing they produced after could match their vintage products. I am currently, and have been for years, running an HT system with all vintage Polk speakers powered by an Emotiva XPA5 and a Lexicon processor.  That said Polk speakers require some power to make them sing but 250w is more than enough to get there with plenty of headroom to spare. It' kind of ironic that you should be driving the speakers with a Yamaha as I experienced similar issues when I had mine mated with a Yamaha processor. The yammy had to go. I also strongly suggest fixing your listening environment before spending a lot of money on equipment. Nothing you buy will sound "right" until the supporting environment is corrected. Doing that will save big future dollars. You might also find it solved your immediate problem. Just saying.  PS: Emotiva does make exellent and affordable equipment in its price range. It will never compete with the higher end equipment and it is not meant to.

Emotiva won't solve your problem.  They are inexpensive amps that try to border on high end.  Your Yamaha receiver probably sounds as good.  You need to go to a better brand and there are many out there at the price of the Emotiva.  I speak from experience as I owned that brand at one time.

I gave them a shot this morning with a Rotel RX-1052 stereo receiver i had laying around. 

I know this is also just mid-fi gear but the polk lsim707s sounded much clearer at lower levels with the rotel stereo receiver even though it is rated at 100 watts per channel. The bass was also less flat. Kindof surprising. 

But yes I know I'm playing with kiddie toys here =). It's hard not to bite when there's a $2,800 sale for 2 polk LSIM707s towers, 2 polk LSIM703s, a polk LSIM706C, and a $1,500 yamaha aventage 3070 receiver that some sites rated as the best home theater receiver of 2017. Seemed like a no brainer.  

After reading all of your commends I would have to agree. I think I will be leaving the powering of these speakers alone, and move towards higher end speakers and gear before giving the amp anymore thought. In a few months I will probably Ebay the bookshelves and center off new in box, and work towards a pair of Kefs or Martin Logans. 

I notice at lower volumes a lot of the imaging and clarity disappears.

That's a problem with the Yamaha. Going to higher power won't help it.

There is this thing called the 'first watt', which is the idea that the first watt of power is the most important. Apparently the Yamaha isn't doing that bit fairly well. I suspect if you look at its specs, at lower power levels the distortion might be quite a bit higher than at higher levels.

Better quality amplification is better at that problem. If you go with tube gear, even better...