I agree with your timeline in terms of the coaching and draft. Yes, those come first. Jazz can't even start negotiating with FA's until July 1. As for our own FA's, those negotiations, especially with Hayward, could extend for quite some time. So you don't just put everything else on hold. And the same with Marvin. He wants to return, but maybe not at what the Jazz may offer (which has to be a pay cut). He may then decide to shop around a bit before deciding Utah is (or is not the best situation).
My second point is that I'm not entirely sure Burks and Kanter should move into the starting lineup. I like Alec coming off the bench (as long as he plays 30 mins). And Enes needs to earn his time with better defense. So if Lindsey can find vets - and I'm not talking RJ-type guys - but if he can find a vet that is starting quality (mid-20's with upside like KOC found in Boozer and Okur), then make an offer. Or maybe the vet replaces Alec as a 6th man.
Jazz need a solid core of 8-9 players for their rotation (3-4 bigs, 3 wings, 2 PG's). I think they have 6 (core-5 + Gobert) and the draft should bring one more. The #23 pick, the early 2nd and Neto may or may not pan out as backups. If they do, and if a FA is signed, then Lindsey has assets to upgrade where needed going forward. Maybe he shops Burke + assets for a better PG. Maybe one of the bigs is moved. Eventually the Jazz need to trade some of their mid-level talent + assets for a potential all-star. Otherwise, Utah treads water as a playoff team but never a contender.