The rule of thumb is to find speakers that you like and then pick an amp/electronics that synergize well with them.
As you are sans an amp pick up a contemporary/decent "used" integrated amp (here @ A'Gon would be a good choice) for $1K or less and run it with the current setup.
Separates are not necessarily better than integrated's.
Hopefully you will find a way to audition a variety speakers whether it be by travel of having them shipped/returned or perhaps you will purchase something on the faith of a review and hit a personal jackpot.
By purchasing something decent used you can then resell it for little loss if you decide to step up to the next level.
It could even be that the new amp will sound quite a bit better than your previous receiver when mated to your current speakers.
This said, I also find the "room correction" amps (mentioned) interesting for your particular situation, but wouldn't spend a bundle on such until you find your fave long term speaker.
DeKay
I