Letīs suppose the characters found JME on the future,take it back to the past and destroyed it.
There will be no need to defeat Ulti then.
Since the machine disappeared from her time and was destroyed on the past she can no longer possess anyone from that time on.
This will not violate the stoneness of time because it will only influence the events after Squall comes back.
Since Ulti needs the machine to perform Time Compression it will end after they destroy it.
The machine would disappear from the future FROM THE TIME OUR CHARACTERS REACH THERE ON,not before.
Attention,I didnīt said TO DESTROY ODINEīs ORIGINAL MODEL.That wouldnīt work (not even be possible).
So a better strategy would be for the doctor to put a magnetic device on the original model of the machine then to make a detector machine for Seedīs(hoping Ulti would not found itīs use).
Using this detector our characters could go directly to the machineīs room (It seems Ulti is not close to the machine.It is working automatically) and steal it quickly enough before the time compression ends temporarilly.
I am assuming that time compression require the machine to still work.
What do you think about the last line (and overall).
This is the kinda mission Seed is used to.Timing missions with coverage(e.g. the missile base).