a typical mast will be fine supported only by the lowers or uppers, as long as the wind is less than hurricane strength.
My boat got a new (keel-stepped) mast because the yard disconnected ALL the shrouds and went home for the night. It then blew over 40 knots and folded the mast over onto the neighboring boats.
I see your point that only the lowers or only the uppers would be OK.
My main question is, do I need to disconnect lowers on both sides evenly, or is it OK to leave them on one side, but disconnect the other to work on them? I wasn't sure if the lop-sided pull would be problematic, or OK for a few hours of work.
By the way, the stinks regarding your mast, but I'm glad to hear you got a new one out of it!