Upvote:3
You can definitely do mobile check in. There is no exit formality for the US. You will not have to do TSA again as T2 and TBT are connected airside via a bus and the ride takes approx 10 minutes depending on traffic. 4h should be MORE than plenty if your flight is somewhat on time. The linked site at the bottom gives a detailed description.
At T2 after security make a right and there's gate 21, you'll keep going right and see the bus lines. Take the one to Terminal B 1XX gates.
Upvote:4
Delta has airside shuttles connecting T2 to T3 and TBIT. (Only since Delta moved from T5/T6 to T2/T3 so some other sources might be outdated and not mention them.)
This article however, is from May 31, 2019 and here it describes how to get from T2 to T3 / TBIT:
After clearing security take a hard right. You’ll see gate 21 — which is an active gate boarding and deplaning flights. Keep venturing right and you’ll see the two shuttle bus queues: one for Terminal 3 (gates 30-39) and the other for TBIT. (Yes, the sign above says gates 130-150 and the one below 120-160…) Escalators or the elevator will take you down to the tarmac. From there, board the bus and grab a seat. The ride from T2 to T3 is about 3 minutes, door to door. It’s about 10 minutes from T2 to TBIT — and then a nice, long walk to the Delta gates.
Long walk -- this blog post mentions the TBIT drop off point is at gate 146, the end of the terminal.
This even more recent flyertalk thread mentions it runs every 15 minutes or so. Also it mentions in T3 it is near gate 35 and points to this useful map on the website of Delta.