No, you don't have to remove the transmission to replace the governor.
First remove the transfer case skid plate, the transmission cross member, front and rear driveshaft, then the transfer case. The governor is easily accessable inside the extention housing (it's already been removed in the picture, you can see one of the holes). Remove the two bolts and replace it.
I changed the valve, governor body (stem) and factory spring. You can see the small aftermarket return spring that I installed, as well as the new larger weight from Sonnex.
Not a very difficult job, should only take a couple hours at the most.
You should tackle the job yourself!