After some feedback from the players I'm not going to try to adapt 5E to my card stack system next month. We'll be sticking with the 3E model, which is a natural for the multi-classing in that mechanic.
After the card stack part of things I ask the players to turn to the person next to them and define their characters relationship, then repeat with the other player, so that every PC knows two other PCs but not all eight or nine PCs. This keeps a degree of party coherence but allows for inter-party conflict as well.
In the first session we did 6th level heroes where one group of questers were petitioning a group of established town-based clerics and thieves for help on something and ended up uncovering a centuries old curse. The second session we did a diplomatic meeting 12th level heroes and political players who uncovered evidence of a planned invasion of the lands under their control who had to plan out how to confirm the threat and counter it. Both were clearly D&D at various stages of play, but had very different feels.
This time around I'm repeating the 'everyone gets to draw geographic features on this map' aspect from the second game but modifying it so that pairs of heroes (the first relationship) are responsible for one quarter of the treasure map. This lets everyone have a say in the sort of adventure they want to engage in and the types of threats they have to face. This certainly makes my job more interesting as I have to improv what those challenges actually are based on the details on the map.
I might also say the second relationship discussions are by definition weaker, lacking a shared motivation for getting the treasure. This will all but guarantee some inter-party conflict when they actually get... whatever it is they're after.
I think I'll try to work this out with 9th level PCs, who in my analysis of the classic O and AD&D design are iconic without being political, just starting to move into politics, land clearing and gaining groups of followers. I think I may institute some new damage mechanics to keep Fighters and melee combat impressive without taking tons of dice rolls (abstracting multiple attacks to greater damage and ability to divide damage between targets). I really want the Fighter heroes to feel like John Carter, Conan and Fafherd - more than capable of moving quietly, donning quick disguises and performing impressive physical feats - rather than armored Arthurian knights since that better fits the treasure map through dangerous terrain goal I'm aiming for here.