Ok. I guess I got confused on the NY17M situation, but I guess it really still goes all the way to Exit 125 (well EB anyway) and backtracks.
Signage there is confusing to say the least. The reference markers on that road to exit 125 have a reference route number on the portion upgraded, but there's a reassurance shield for NY 17M just past where old exit 125 was - only to have "TO NY 17M" at South Street. There are also uncovered I-86 shields there, so I'm not sure I'd take the signage as gospel.
At least westbound is consistently signed, although it seems like westbound may have always been signed to exit 124. I'm starting to think that NYSDOT might have ignored the impact to NY 17M and that it might just be discontinuous eastbound now.