Bob,
Someone else is going to give you better advice, I’m sure. But if you need a quick, easy solution, I’ll tell you what I’d do:
I would have a time stamp attached to each of the files (slaves and masters alike). The slaves might have identifiers but I would try to get away from having them with individuals’ names on them. The master would have “-Master
” somewhere in the file name: 202506-072220-202506-072219-ProjectTW-Master
. Note the two date stamps: the first being the update and the second being the “thread” or “version” (I don’t mean the TW version; rather: YOUR team’s TW version).
The slaves would have something like: 202506-072203-202506-072219-ProjectTW-25
(25 denoting the team member). You, if you are the leader, could have “1” for your own slave version.
Team members (slaves, including you) can upload your slave versions to the server or other storage. That would mean a lot of backups and versions. But you would know which ones are the later versions from the file names. They would never be overwritten. Just archived.
But to resolve this issue of having slave TWs having tiddlers that are not in the latest “-Master” TW, I would ask that all team members (including yourself) “dump” all the latest relevant tiddlers onto the file server as well (JSON files), which, in turn have their own "time stamps, -Master /-Slave, title". What you’ll get is a tonne of tiddlers and TWs on the server. But when you update the “-Master” tiddler, you’ll know which tiddler JSONs to pick from.
Everyone on the team would have access to the latest “-Master TW” and could themselves compare whether their “relevant” tiddlers made it successfully to the “-Master”.
It is, in fact what I do personally, even though I’m the only active “team” member. (Like everyone else here, I use multiple computers and devices. But unlike everyone else I DO NOT USE CLOUD or server storage.) The other member being my wife, who has little interest in TWing. 
You’ll soon get a genius coding /script solution and possibly a plugin solution that’s way better than the one above. But, this is my two cents.