Urban myth about checkpoints. TSA policy on this changed four years ago. With some extraordinarily limited circumstances, a valid BP to any gate at the station, gets you access to any checkpoint, whether or not that checkpoint has an airside connection to your departure gate.
This does not mean that: 1) that your carrier will allow you access to whatever passes for priority access; or 2) that an Officer won't point out that you are at the "wrong" checkpoint.
That said, for OP's stated reason, access to E is a worthless PITA given the other options.