A good solution to this problem is to use an SSH Certificate Authority - then you need only configure the CA certificate on each box, and you can either issue semi-long-lived certificates to each user who needs access, or use something like Vault to issue short-lived certificates intended for one-time use.
This model is described in an excellent post by Facebook from a while back [1].
(Disclaimer: I used to work at HashiCorp, and put this model into production there, though the Vault support for issuing short-lived certificates was added after I left)
[1]: https://code.facebook.com/posts/365787980419535/scalable-and...