What can come after Apogee Divas?

Rogerwalk: Not knowing the Dynaudios, I tend to agree with Kirk, above. I would add, however, that the Quads will also outperform the Divas, even more perceptibly so in two channel classical IMO. Pls note though, they require VERY strong & controlled amplification, patience, and maintenance -- but the musical rewards are very high. (BTW, Quads are stats whereas your Divas are passive dipoles -- so, different sound.) The Quads as part of a multichannel HT is another matter and I don't know if they can take the spl usually associated with the likes of Gladiator et alia.
Another non-dynamic design you could consider is a full-range Soundlab. Good luck!

Fact is, Detlof, I have *literally* taken the words out of your mouth (or posts, as it were)! Unlike you, I never managed to reproduce those high frequencies with my 63s --due to insufficient amplification, as you have noted elsewhere.
Rogerwalk: if you buy Quads you now know who the specialist is!
To put the "flat-speakers" case bluntly, there's no musical comparison between the two, IMHO and having lived with Apogees (internal c/over, however) & Quads very many years ago. This said, I humbly submit that Divas are beautiful all-rounders, indeed, great speakers and, as you intimate, difficult to match -- more so to surpass!
Cheers