SAM still works to fix push notifications. It just doesnt work to actually unlock the phone anymore. Doing that will fix your battery drain.
If you can get 5.12 baseband back on there you can make a custom 4.2.1 with pwnage tool or snowbreeze and restore to that to preserve your baseband.
4.1 did not come with 5.13 baseband. 4.0/4.0.1/4.0.2 did.