I'm not that well versed in the Polk floor models, but it's a respected brand. My fear or concern with speakers in this price point... they probably will sound a little better than your Pioneers, but I don't know if they will ultimately check all your boxes.
For you, I would be looking at the Klipsch RF7-iii....very sensitive, they play loud and reasonably accurate given how loud you might be playing them. Yes, they are more than double your budget, but I would wait and save up a bit more if I liked them.
Most of my advice or suggestions on this forum stem from my personal experience. and this one is no different. Two years ago I was ready to upgrade my 20+ year old audio system...my speakers (B&W 804m) were great 20 yrs ago, but I was ready for a more neutral speaker...long story short, the 1st month or so of demoing speakers in the $1500 to $2500 a pair range...there was very little if any appreciable difference in sound quality...it wasn't until I started demoing speakers that were in the $3k to $6k range that I started to hear more transparent, neutral sounding speakers.
I'm not saying you need to buy the Klipsch I mentioned, but make yourself a demo thumb drive and play the same songs on every speaker you demo. Some speakers that right now might not be in your price range, but time is on your side I think, it won't hurt to listen to a few of them.
Good luck with it.