Have you ever actually worked in HR? Doesn't seem like it. Yes, keying anything in takes a few moments. However the work doesn't revolve around one TM. HR has to deal with the entire store. All I'm saying is we don't know the full details of what happened and the routines of OP's store. If OP handed in their resignation on a Tuesday, there's no way in hell it's going to be keyed in before the new schedule generates in myTime. For those of you that hav enever written a schedule, it generates at noon on Tuesdays. You schedule writer has until Thursday at noon to edit it before it's published. This is also why all time off requests and availability changes are supposed to be submitted by Monday. Something else to consider: HR may prefer to have conversations with TMs resigning before putting it into the system. My ETL-HR does that with everyone. So there's sometimes delay between the resignation being turned in and being keyed in.
Just to re-iterate: OP is in no way responsible for finding coverage for those shifts. They can still leave on the 7th without being penalized. OP is interested in keeping the option open to return later, if they want to. With this in mind, I would look for a way to stand out from all other TMs that might want to return and from other potential new TMs. OP can do this by taking literally 2 minutes to put the shifts on the swap board, inform HR, and walk away. I'm not suggesting that OP go up to their TMs and asking them to cover the shifts. Write down the shifts. Talk to HR. Walk away. Simple.