I've never found a clear cut answer to how lease obligations are handled upon death. It would surprise me if the estate wasn't liable on the lease if it is solvent. But I did have a landlord tell me they couldn't proceed against the estate even if it wasn't paying rent (that was a clearly insolvent estate).
If I were advising you (and the way I have handled this for estate clients in the past) I would probably consider any back rent due as of the DOD as a creditor claim that would have to be submitted as such in the probate proceeding and be subject to proration if the estate ends up insolvent.
Starting from the date after the tenant died, it would seem to me that the best way to look at it would be that an involuntary assignment of the tenant's rights and obligations to the estate occurred, with the post-mortem rent payments treated as expenses of administration (they have the highest priority and come out even if the estate is not fully solvent to pay pre-mortem creditor claims). The estate is going to probably need a little time to clear things out, so why not find out how long, come to an understanding and rent it to them. It can be a month to month arangement if it goes beyond 6/30. That way you know when you have to re-lease it and can plan for that.
Whether the estate can terminate the lease early I just don't know. I don't think so. But as long as they gave me reasonable notice I wouldn't press the issue.
Here's a couple of stories about the non-legal public relations aspects of playing hard ball with a dead person's estate: