Is the UPB greater than the property is worth? You can't just set the reserve amount without records supporting it. You are correct on doing due diligence on prior liens. You should also check that the seller has proper chain of ownership of the mortgage. There are a lot of issues that can delay or stop your foreclosure from happening. Just because the original borrowers are deceased, doesn't mean no one has standing to challenge the foreclosure. Is there a right of redemption in your state? You should definitely hire an attorney to conduct the due diligence and talk you through the foreclosure process. There may be a lot more uncertainty than has been presented to you. FYI, I'm no longer a practicing (or licensed) attorney, so none of this is intended to be legal advice. These are just some of the issues you want to get clear on before trying something like this. If it's really just 60-90 days, why not buy the home at the foreclosure sale?
If the heirs really want nothing to do with it, and there aren't junior liens, you may be better off paying the estate a nominal fee for their interest in the property, and negotiating a payoff with the note seller. This could take a lot of time and uncertainty out of the process, depending on the answers to all the questions above.