Shane Please take care when you do this work.
Every part has to be accounted for.
Get in an area that you will have room to layout the parts .
4x8 sheet of plywood and lay down a sheet of plastic over it.
get some storage containers with covers so nothing will be lost and make or take digital images as you are disassembling. This will help when you go to reassemble.

First see if that lever is fully engaging by removing the control cable and move the lever by hand
Drain the transmission oil Look for steel shavings. or clumps of gear parts.

GET A REPAIR MANUAL EBAY OR FROM A SUZUKI DEALER. Best to have the Manufacturers it shows more details.

Were you able to get that URL site and look at everything first.
Print the stuff out with the parts list and study it befor you start taking the transmission apart

 

This is a major job you are to embark on.

Clean Clean Clean Use keresine or diesel fuel--- not gas of carb cleaner.
To avoid drying the bearing and shaft surfaces.
When you reassembel have an oil can containing the same type of lub fluid you will be putting back in the machine and oil each part as you assemble.

By The Way this will mean all the parts head cluthc sidecases all have to come apart.
SO MAke sure that it is the transmission and mot the mechanisms that shift the gears that are easire to get at.

 

Need to bring this thread back up as I am having the same issue where it is stuck in Super Low. It was nothing simple in the sub transmission. I have taken everything apart meaning splittting the cases and still do not seen anything ovbious in either any transmission. Anyone have any ideas before I box this thing up and put it at the curb?