It’s not feasible, especially if trains are coming from the north. trains coming from the south can relay at Bergen Lower, but would have to go out of service at Carroll St, which would make them useless. You can have some trains coming from the south can stop at Jay St, but they can’t turn at Jay because they would be the outside tracks there. They’d have to continue to York before they can turn back south.
But with Rutgers, I think you can have a split , like the split we had when Montague was being rehabbed. On weekdays, you run the to Delancey, like you proposed. Then you have a second service from York to Stillwell. Then on weekends/late nights, have one continuous service that diverts via the from West 4th to Jay (like how the weekend went over the bridge in 2013-14). It would require East Broadway to be closed full time and Delancey and 2nd Avenue to be closed on weekends and overnight hours.