@robla The feedback I've heard from various stakeholders and reformers across the landscape is that many people oppose narrowing the field too much, which can prevent minor parties from having a meaningful voice in the general or being seen as viable. Being on the general ballot is an important part of the path to becoming viable for a third party.
For that reason, I think there's more consensus around advancing a set number of candidates to the general (instead of setting an approval threshold). Given that the voting method does fine with multiple viable candidates, I think advancing the top 4, 5 or 6 is totally reasonable. The upper limit is set by voter fatigue.
I think two stage Approval is generally the way to go for Approval elections. Approval Top-Two makes a lot of sense for jurisdictions that already have Top-Two, but all other things being equal I'd recommend Approval Top-5 or Top-4. I'm not sure if an even number is better or not, but that's something that should be studied and modeled for each system.
For STAR I generally recommend having a conditional primary, where the top 5 (or 4) advance. And, if less candidates than that register you just skip the primary all together, which saves a bunch of money.