It's an even more tedious process but you could always cook up a custom restore package with your game save data and restore from that (using iBackupbot). I'm sure there are other tools out there too
I personally don't care that much about game save data. And the ones I do seem to utilize some sort of cloud backup
To the OP: generally speaking, you won't have any problems. I would say it helps if you made a backup after you removed all your jailbreak tweaks though. The only problem I would really see is that all the jailbreak junk and clutter will be placed on the new phone with no way to selectively remove them
Meaning, you would have to start as new or cook up a custom restore package to remove the jailbreak junk or else your "other" would be higher than a non-jailbroken device