Hello Joshua,
I understood that downtime is importannt for you.
How much is your DB size?
If you do migration like below you will have minimized downtime.
1- Install new OS with the same hostname but different IP and isolate your new OS from your old network. In order not to have hostname conflict.
2- Install DB instance
3- Copy your system with one of your old backup with the same SID. Copy all folders, profiles etc to your new system. Change the parameters according to your new systems size.
4- stop new system
5- Take online backup of your old system and keep your log backup for restore on new system
6- Restore the DB with recovery mode to your new system
7- Apply all log files to your new system
7- Start downtime on your old system
8- Take the last log backup of your system.
9- Apply the last log of your old system
10- Shutdown your old system
11- Change the IP of your new system to old IP
12- Allow network connection to your new system
13- Start SAP on your new system.
Your system will be down for only the time needed for applying the last log file and changing the IP off your new system to old IP.
Hostname, IP and SID are the same so all connections from external systems will have no problem.
Regards,
Yuksel AKCINAR