My vote would be to add dual subs. The ST's are really great speakers, but physics is physics. Four 5" drivers are not going to get things done. In my experience, the TL alignment gives an illusion of good bass by accenting the lower frequencies. What they typically lack is midbass, which can make them sound a bit thin (or lacking a full sound). Proper setup is key, and it's VERY tough. You say your speakers are "as well placed as they can be." That tells me they can't be ideally placed, which is almost always the case. Properly placed, and EQ'd subs can be magical, and likely what you need. You have the receiver for bass management, so subs is what I'd do first.
The second benefit to subs is offloading the low frequency bass content from the ST's will clear up the midrange considerably. Again, physics come into play here. Asking those (4) 5" drivers to play clean midrange AND play the lowest octaves increases distortion to a very audible level.
If you decide to go with an amp, fine. Just realize that it is a stepping stone to needing a good preamp, and likely one like the P7 mentioned for multichannel content. If you are looking for 2-channel performance, that's another story. Then I would get an amp only for the front left and right channels. Leave the center channel and surrounds for the receiver to drive. Then a nice 2-channel preamp with HT-bypass is the way to go.
I'm also in the camp that receivers are absolutely the worst for sound quality. Even feeding my $2,000.00 Onkyo receiver with the best source and DAC I've ever had gives me a sound I personally find unlistenable. Of course you have to factor in that I'm now spoiled. A receiver can sound fine as long as you havent heard better. Once you do, your screwed.
None of the above addresses the source. That is yet another significant factor. But as stated above, I wouldn't want a great source feeding a receiver as it's likely a waste.
Good luck with whatever you decide to do.