To determine if it is trans related or somewhere else, pull the driveshaft and try your push test.
Fluid alone won't cause the problem, but a bushing or planetary gearset in the trans may be going bad or galling itself up, creating friction where there is supposed to not be.
If it pushes hard with the driveshaft out, then look at the rear end or brakes for an issue, as the earlier post suggests.
Problems with the posi unit would not show when pushing in a straight line, only show up when turning.....just like pushing a racecar with a locked spool around a corner, the locked rear makes pushing and turning at the same time a real chore to those who are pushing LOL.
Brake or wheel bearing problems, wont matter if you are pushing straight or around a corner.