Integrated amp recommendation

Your speakers are 4 ohm. Likely they drop below this at lower frequencies. Maybe that accounts for the comment you made regarding the bass being somewhat lacking. I would look for an amplifier that delivers 100wpc at 8ohms and close to 200 at 4ohms. I agree that the $500 budget  increase will provide a greater return on your investment.

If interested in the Rouge Sphinx I would look into the V3. It sells for ~$1600-$1800 . Audio Advisor sometimes have an open box unit for sale just under $1500. 

Buying use opens up possibilities, as per the several suggestions aforementioned.

Good luck in your quest and keep us posted.

Belles Aria are under $1500 used....if you want to keep costs down, Musical Fidelity M2si...I have owned both...

From what I have read, the Hegel, Ayre (also this one), and Belles recommendations stand out for quality. Rogue, too, but perhaps not at the same level. Black Ice also gets some good reviews. As does Schiit.

Please don't get a Cyrus. I had one years ago and it was awful. 

Highly suggest the $1500 price point - either the Rogue Sphinx v3 or the Schiit Ragnarok. Both have phono pre amp but Sphinx probably a better choice overall - it's the highest rated entry level integrated in history (probably). I bought one for my son and was completely impressed. I run the Schiit Freya+ into monoblocks - wish the Ragnarok had tubes and MC phono but the DAC option makes it standout a bit too as Schiit has amazing DACs for the $$$