Attacked the Snapper 28088TE this afternoon and got the shift mechanism figured out. I thought about using a vice with 2 sockets, but then I dropped my 2 arm puller on my foot and had a great idea.
See the front and side view jpgs. for my use of a 2 arm puller. It made the spring compression easy-peasy. Fortunately the shaft had a hole that fit the puller screw perfectly. I cranked it down until the shim and lock pin could be installed. then after decompressing the spring installed the cotter pin. Et Viola!
After assembly I bolted it back onto the main frame then installed a new linkage, boots, driven wheel and brake. Tomorrow I'll hang the deck back on it and start on the engine carb adjustments. Might be mowing some grass if all goes well.