Recommendations on Patch Management for RHEL Servers that haven't been patched in years

So I'm in the final phases of ingesting iso updates for our RH Satellite Server and adding RHEL Servers to it.

The next level is the ugly reality of catching up our servers from years of missing patches so they are secure and improve performance.

I'm aware of change management, patching during off hours, communicating with the stake-holders about patches, and making snapshots from VMWare/backups. However I've not been in a situation like this before where the servers have been unpatched for years and years.

It would be really dumb patch all at once, and it would cause issues. My question is does anyone here any recommendations on how to move forward with a daunting task like this?

thanks