I've had the 650A a couple of weeks now and I've tried a wide range of speakers with it (I've got 6 different sets here, including the MS902i).
I've come to the same conclusion as Hi-Fi+ did in their review of the 650 components, in that I feel the amp works best with good quality soft-dome tweetered speakers, rather than those with a metal tweeter such as the Mordaunt-Shorts or my Mission 751s (the Missions work a lot better than the 902is because the tweeter is much higher quality). One exception to this is the MS Mezzo 2s. The Mezzos are a good step up from the Avianos and the tweeter seems more controlled, with better integration across the entire frequency range. Not a great deal more money than the Aviano 2 either.
I don't believe changing to the Avianos would be a good step. Essentially they are a development of the Avants you already have and, good though they are, I think you can do better synergy-wise.
The Quad 11Ls love the 650A. It provides all the power they need whilst the speakers make the most of the detail and spaciousness of the amp. Its a very dynamic combination that never strays into harshness. I have done A/B comparisons between the Quads and the 902is, and the difference is huge.
The other speakers that might be worth trying would be the EB Acoustics EB1. I haven't heard them but WHF rate them very highly, they have a good design team behind them and, looking at the specs, I suspect they could make an excellent match to the 650A.
I don't actually think the 650A is that easy to match but, trust me, it really is worth the effort.