Beside what rr503 said about NJT (permanent deal breaker without adding 2 additional tracks from Jersey to tie-in point) and the pipeline (which can be negated with cubic dollars), it took all of two minutes on google maps to confirm that neither the Shortcut underpass south of Mountainville or the Newburgh Branch underpass at Vails Gate Junction still exist. By asking about the east side of the thruway, are you asking about building on the east side further south of the Mountainville underpass to go under the thruway closer to Newburgh Junction? Most of the Shortcut was on the east side to begin with. Seems like any reconstruction of the Shortcut would be difficult given the ROW is partly public roads now and developement of Central Valley would prohibit a tie-ie at Newburgh Jct - you'd have to tie in just north of Central Valley. Also, CSX is currently in the process of double-tracking most of the River Line, so any rerouting would have to accommodate double track for freight, so add a few more baskets of cash.
Other problem with the Shortline is it uses the Newburgh Branch to get to the River Line in Newburgh, which involves sharp curves on 4 miles of grade that's mostly over 1.1%, well over anything else on the River Line. Not an improvement for freight trains. It might be OK for commuter trains if you were looking to get passenger service to Newburgh, but CSX probably would laugh at you.
Rerouting the River Line traffic doesn't seem like a happening project to me with the poor tie-in at Newburgh and the $2B-$3B price tag (at least 70 miles of new double track, 20-25 miles of ROW acquisition and the cost of totally renegotiating/disrupting the RRs and governments involved).