much easier fix:
have a "pre-game" that's about ~10 seconds long (also, preferably, not the kind of pregame wherein medic gets uber in like ten seconds), wherein spawn doors don't open until they're finished, players can fuck around as they please in the spawn until the round starts, and demos/sollies can prepare as needed right next to the door
lets you have a gap of time to work with, will also slightly buff other classes' rollout speeds, and it means that nobody has to give a shit about where they specifically spawned in the spawn room because honestly that's never a thing ppl should care about