The place I am suggesting there is a grease nipple but which could get tight due to corrosion if not regularly greased is where the shift lever shaft enters the top of the exhaust housing. Lesser makes do not have the greaser and often get tight, so tight that people break the shift lever.
Look at the mid section parts diagram in the BRP parts catalog
epc.brp.com
I am wondering if there is any thing wrong with the linkages between the shift lever and the shift rod but you'd have to remove the power head to look at them.
The shift rod passes through an O ring seal below a pressed in bush in the top of the gearcase If there was not a seal there water would get in and the oil would get out!
See parts # 8 and #10 in this diagram
epc.brp.com
Also wondering if you have bent the shift rod.. If the bends in it where increased it would make it effectively shorter so that might not engage with the clutch spring, which is what happens when you shift into neutral on these little gearcases