With recent experience and discoveries, I would avoid stuff with switching power supplies such as the Mytek Brooklyn or Benchmark dacs. I have been in close communication with another user (robelvick) who initially went with a Benchmark DAC2 HGC and then moved over to a PS Audio Stellar Gain. The Stellar Gain was a significant upgrade in sound quality. The Benchmark has switching power supply with op amps, while the Stellar Gain is linear power supply with discrete Class A analog stages. The difference is significant. I have not personally heard the Stellar Gain, but my experiences with different topologies in general would agree that the Stellar Gain is superior.
I'm sure there are several available options, but the Stellar Gain would be an excellent choice. The Parasound P7 is very nice, but it will not be as good as the Stellar Gain. However, the P7 does have a phono preamp built into it.
Another option would be to look at some of the Audio-GD balanced DAC/premps, such as NFB-27.77. Like Stellar Gain, it will be a superior DAC/preamp, but you will still need an off-board phono preamp.
The Adcom 555 is definitely a serious weak link here, so upgrading the amp is an excellent idea.