So much wrong with this it's hard to know where to start so I'll simplify. What I propose IS using AVP with an external amp, at least for the front. And the IIIa's do have deep base, deep enough to need careful crossing over etc. Finally, I've compared the 3800 with the Schiit stack as well as it's predecessor system (Krell, custom Sonic Frontiers stuff, etc). The 3800 isn't even in the same category. Why you think that AVR would deliver better 2ch performance is a mystery for us all to ponder. Maybe time to get your hearing checked.
If you are going to use an AVP for the front, then you are best using all external amps for all speakers. That is your best bet. That is exactly what I do. You listed and AVR and not an AVP.
If you are going state of the art like I do, then you need a good AVP and external amps and not an AVR.
I can understand problems with integrating the Maggies with a sub. They are membrane speakers with a figure of 8 distribution and a null at the sides, with the rear radiation out of phase with the front. In addition they are non resonant and very low Q speakers. So they are truly non resonant.
This problem is shared with the Quad ESLs which are the ultimate flat diaphragm speakers.
Peter Walker solved this by working with the Finish firm Gradient to produce an open baffle figure of 8 sub. Whilst this is not essential, if you are going to use a sub it needs to be ultra low Q. Pretty much all commercial subs are high Q. In fact most wantonly high Q. So much so that I personally could not live with most commercial speakers and especially the subs.
I build my own speakers and specialize in low Q transmission line speakers. My designs though are totally integrated and designed as functioning seamless systems from top to bottom. They are way out of the commercial norms, but all for good and viable reasons.
Auto Eq systems are not going to solve this problem for you.
The reason is that you can not design a really low Q reflex ported sub, or it would not work.
If you made a really low Q sealed unit and you can, it will have a higher than desired F3 unless you have a really costly driver and the Eq required will need a monster amp. These subs exist but are really costly.