I agree it's no problem when the competing rate has bkfst.

I'll add that you won't get breakfast in your new LNF rate. Some people have reported being able to get the LNF team to add it by putting something in the notes or sending an email later. That didn't work for me. Ideally, you'd find a rate on MR.com with breakfast and LNF to that (try entering ADP or ADV). Even if it's not the lowest non-refundable rate, it should work and you'll keep breakfast.

Your other issue is trickier. You said "It looks like there's no 24 hour refund period with this rate". I'm assuming that "this" refers to the MR rate (the other way around is probably non-problematic). If the LNF failed, you can ask MR to cancel the uncancellable reservation, without charging you (I did it successfully once, albeit in a totally different situation where my flight was cancelled and I was staying in a different MR hotel that night). Having filed a claim and pdf's the competing rate might help. Has anyone done this after an unsuccessful LNF claim? Well, if you do go ahead, at least make 100% sure that the competing rate is not on a "voucher" site. You could also leave some notes in the LNF claim to "please cancel this reservation if the claim is not approved" though I've never heard of anyone trying that.