I've never tried using Helium to transfer between phones, but it might not complain that you're restoring to the wrong phone. (Titanium does.)
Back up all the apps. The default is to just back up the data. You can do that and back up the apps using another program (I have all my apps backed up with App Backup & Restore, so I only back up data with Helium). But you can tell Helium to back up the apps too, so when you restore it's a "press once, go to a long lunch" operation.
You'll need to download a program to run on your computer, and have the phone connected to the computer, when you do the backup, since the phone isn't rooted. There are full instructions.
(Both programs, Helium and AB&R, are free at Play.)