I have done this on another platform in the past. I have not done it on gymlytics before but I'm sure it would work and if you are interested I'd be glad to figure it out on gymlytics and be the commissioner of the draft. We would decide on a day to do our draft and then take turns choosing our gymnasts. Each person would get so much time to choose their gymnasts, (like 30 minutes). Once their time is up the next person in line gets to choose. I like doing it live better because you can better determine what gymnasts you need to draft based on what gymnasts you have already gotten and what gymnasts are still available.
I've checked it out and we would just create a league, a draft order, then agree on a set day/time to start our draft, a set amount of time for each person to add their most recent draft pick and then we start drafting. We would need at least 10 people to join. If you're interested here's a link to a new league I just created called LiveDraftLeague: www.gymlytics.io/join-team/cm4a20tnz000hl70c7pevq7ky