Yes I understand that was you intent but, as the 24-inch model are fairly new, it may take a while for another user int he same situation see you issue and respond.
I don't like these Catch-22 scenarios either but I know for work experience why they do it—hidden damage. Some customers fail to see the part on the estimate that says "this is and estimate and more damage may be found inside, changing the initial estimate". This is probably why they want schedule the repair so they can make sure nothing else is require repair. Example: if tiny shards of broken glass were found to have made heir way inside the case. Best prectice says they should be removed.
I would think a modern insurance carrier could work with that because that "inspect and re-estimate" process is de rigueur on automotive collision repairs.
Can you take it to an Apple Authorized Service Provider or other independent repairt shop? They may be easy to work with.