Backup MX record with same public IP?
Your setup isn't clear: if these are home servers, isn't there a router routing all mail requests to one of your servers? 

Still, to (partially) provide an answer to your question, in your situation, you shouldn't worry about losing email: according to RFC 2821, section 4.5.4.1 about Sending Strategy: 


  Retries continue until the message is transmitted or the sender gives
     up; the give-up time generally needs to be at least 4-5 days. […]


RFC 5321 adds: 


  It MAY
     be appropriate to set a shorter maximum number of retries for non-
     delivery notifications and equivalent error messages than for
     standard messages.


So you should have 4 days before losing your email. Then, if you're using a router, you could just make it route incoming traffic to email port to the backup MX server in case you need to do maintenance work on the primary one.