how to automate public key authentication when server dual-boots two linuxes

I have a hopefully simple question on setup for sshd.

I recently switched my server from rshd to sshd and it works fine. I am using public key authentication.

However the wrinkle is that this server has two different linux partitions which I need to alternate between (strictly only one at a time, not a virtual machine setup). With rshd they both appeared to be identical as far as rsh authentication. With sshd, when I booted the second one, and then tried an ssh to it from another machine, of course I got

... rsa fingerprint ... etc etc.

I realize that this is exactly what sshd is designed to do, to detact impersonation of the server, but unfortunately that's exactly what I need to do (but of course don't want any other impersonator to be recognized).

I could try just overwriting the second server partition's
with the first one - but is that the right way? Would that cause other problems? Hoping someone else has come across this and there is some recognized solution to this.