I'd put the emphasis on which integrated sounds best to you with your speakers and that it can drive them effectively (nice speaks BTW). With monitors and a good integrated you may find you don't even need bass management for 2-channel listening. But if you want it you can always add it later with something from DSpeaker, etc. By requiring bass management in an integrated amp you're cutting down your options to a relative few, maybe unnecessarily.
You should start by identifying what aspects of sound reproduction are most important to you and/or that you'd like to improve upon (i.e. Imaging/soundstaging, detail, tonality, etc.) , then gravitate toward integrateds that excel in those areas by reading reviews, forums, etc. Just because your AVR is from Anthem does not mean your integrated needs to be too. Best of luck.