You don't say if it is still under warrantee? If it is, Grizzly I would bet would contract with a local rebuilder and they would fix it for you. Also when are you shifting? Many times they tell you to shift when the machine is running or with the power off put a hand on the chuck and wiggle the chuck back and forth when trying to shift. Have you called Grizzly and talked to customer service? They may have a procedure sheet on what to do. Have you oiled it?
If it isn't under warrantee, first study the manual first, gather together some metric Allen and end wrenches, some plastic bags to store the parts, Mark the bags with where they came off, take pictures as it comes apart. Before opening it up, put the levers in the lowest feed rate and after you pull off the cover take a picture of where the gears are located. From the manual it looks like there are brass shoes that move the gears.
I would buy a small smooth cut file or a jewelers file so you can file the burrs off keyways and shafts so you can move the gears by hand and no stiffness while sliding them. When assembling you may have to anchor the brass shifters with a dab of grease. Putting it in the lowest position os now important as it will be easy to look at the picture you took and locate the handle and gear positions. Be sure to scrape off any Silicone or carefully remove any paper gaskets. When assembling spread a thin layer of fresh blue / industrial Silicone on the covers. Be prepared is the key to a simple but tedious project. Rich