Speakers replace or improve?

3. You’d need to get a second amp to bi-amp, preferably one with adjustable gain so you could vary the woofer output relative to mid/highs.

I personally doubt the Polks are worth it if they don’t have plenty of bass on their own as-is. It’s subjective however...if you otherwise flat out love their sound, maybe it’s worth the effort, but the term "The treble and mids are ok..." that you used speaks volumes.  The goal is to love your system, and that'll always be a struggle  if two thirds of the key ingredients are only "ok"....regardless if you get the bass output up to snuff.

2. GR-Research has a kit called the Brute that would come in close to budget ($1200+ s/h/tax), and should have plenty of slam, and likely better overall clarity and soundstage.

1. Not a big fan of EQ, and know diddly about DSP and other such options, so I’m not much help with that option.

I would say you can invest in either the integrated amp or speakers and get a very big improvement.
 

I think you will likely get the biggest boost by upgrading the integrated amp. Reach as high as you can… maybe a used NAD or Rotel integrated amp. No extras. If you can get something that originally cost $3K… it will have a huge improvement in the current it can supply and take control of those woofers. Do not add an equalizer. It is symptomatic relief that doesn’t contribute to eliminating cause. 
 

Simple NAD and Rotel integrated amps (no extra functions… DACs. Streamer…etc) are built with sound quality in mind. Integrated amps will sound significantly better… and shockingly, by doubling the investment from <$1K (carefully chosen for sonic performance) to well over $20K. 

1. No

2. Probably not. Although, I’ve a sneaking suspicion that you are expecting room-shaking bass. Are you sure they are wired correctly? Out of phase connections will have poor bass. I think you need to connect the sub somehow and reappraise. Otherwise, better amplification is on the cards.

Thanks a lot for all your answers and suggestions. I am sure the speakers are wired correctly. I checked that several times.

Occasionally, when I am lazy, I play CDs using my old Sony CD CDP-CE415. It is also connected to the same amp and the speakers. The bass is much better when I play compacts. Maybe I need to get a decent preamp?

I am not expecting room-shaking bass. I just want to hear the bass when I play vinyl records.

I think I will connect the subwoofer for now until I find the best solution for my problem.

Before I make any investments I will try few things.

1. I will try to temporary swap the YAMAHA amp with my 28 years old Sony STR-D665 which has bass boost option. It sits in my basement and plays very well with my 20 something years old Sony SS-MF315 speakers.

2. I will try to use the Sony STR-D665 as a second amp for bi-amp option.

3. I will try to temporary swap Polk Audio speakers with my old Sony speakers to see if the problem with the speakers.