We have long running processes that were initiated by users who are now inactive

If it is simply a matter of a few processes I believe you could take the manual approach and go in as administrator and reassign these to active users. If you need a more automated approach then this might be something where you could create some process-backed records and loop through those pulling out the assigned to user and replacing that value with something correct. I haven't done this before so I would need to defer to someone who has some experience with automating updates to in-flight processes.

Not sure if it's a valid option but perhaps to reduce the amount of effort you also might kill/cancel some of these older workflows as they are stale.

By process upgrade do you mean this smart service?...

forum.appian.com/.../summary

You should be able to create a new version with the correct assignment then use this to upgrade running instances and then to re-start the tasks that have failed. You could try using a Task report to identify the instances which need the re-assigned tasks re-starting.