I have some reservations about pure turn count minimization in Civ VII, mainly related to the jump in age progress you get from eliminating a civ. Especially in the Antiquity Era, this could drive the optimal strategy toward "wipe two civs as fast as possible"*. It's true that focusing on warmongering sacrifices other things, but the nature of accelerating yields across eras means that getting out of Antiquity ASAP is desirable.
*(It's probably less of an issue in Exploration Era, since player progress on the legacy tracks contributes more toward age progress there).
GotM 2 had some issues, but I really enjoyed the Modern Era in that one. Trying to balance "get your target victory ASAP" with "pick up extra legacy points along the way" added a lot of interesting tension, and I think that aspect is worth exploring further. So I would endorse "total turns minus total legacy points" as a metric to try for future GotMs. I think that even there, it could turn out that turn count minimization dominates, and that a more balanced target could weight legacy points higher (e.g., subtract 2x legacy points instead). But that's a future balancing consideration, not a starting point.
"What to do about mementos?" is also a big question, and it looks like so far the mods have chosen to lock everyone into some generically available mementos as a solution. Personally, I would prefer allowing players to choose whatever mementos they like. There are several reasons for this:
1. Selecting mementos is an interesting layer of strategy that everyone misses out on if we have locked mementos.
2. (Hot take): If there is a memento balance issue, it's that most mementos are simply worse than the generic attribute point ones. If my assessment is accurate, then there really isn't anything to be concerned about w/r/t people being advantaged by grinding out locked mementos.
3. While there is technically a competitive element to GotM, it is more about having a shared goal to provide meaningful strategic exploration. If it turns out that some mementos are OP, so be it. Finding out that information is fun!