I’m interested to hear if you think the STR would be a "laughable" pairing for the Il Cremonese?
No, not at all (for now anyway — read on). In fact, as you’re already familiar with the the sound of the Anthem gear I’d highly recommend you continue to use it with the new speakers for a couple months and let your ears/brain settle in to the new sound. You probably know this, but if the speakers are new you should wait at least 200 hours of playing time before making any firm conclusions. Now, after the speakers are broken in and you feel confident you know the sound as it exists, identify which areas you’d like to improve upon and then do research to find equipment that has strengths in those areas. Moving too fast and trying to choose any equipment now is at least a waste of time and worse you could end up with a combo of gear that doesn’t ultimately synergize to your tastes/liking. That’s why you need to set a firm baseline with the Anthem gear and then determine the direction you want/need to go. BTW, when you’re listening in 2-channel do NOT employ the Anthem room correction because your new stereo preamp or integrated stereo amp won’t have it and you need a pure apples-to-apples comparison here.
As you alluded to, with speakers at this level you’ll want a separate DAC, stereo preamp and amp (yes you are going to replace the STR), or a kick-ass integrated amp. Obviously you’ll keep the AVM90 for HT duties and run its front L/R preouts to the stereo pre or integrated so there’s that. Once you’ve acclimated to the new speakers and determine what direction you want to go sonically start looking/researching for the components above that go in that direction. By all means do not rush this process or you could very well make some potentially bad — and very expensive — decisions you may really regret. Take your time, enjoy the process/search, and get it right. It’ll pay off huge in the long run, and these speakers deserve the effort.
BTW, why the II Cremonese? Have you heard them? There are many phenomenal speakers in that price range from the likes of Magico, Wilson, Rockport, Joseph Audio, Vandersteen, Usher, Raidho, etc. out there and are well worth auditioning just for perspective if nothing else if you haven’t already. Anyway, just my $0.02 FWIW.