There is a special tool to remove and replace the output flange. Make your own or buy from the several after market tool suppliers. I use tools from Cycle Works a bunch. I have the flange puller from them.
However this tool doesn't seem to be in the catalog anymore. maybe Dan has some or will make more? You could always ask. Maybe I don't know how the read the catalog?
It does sound like the problem is the dogs on the Lay shaft. But you have to look. $100 for those two parts is a good enough deal that I think I'd get them now before they disappear anyway.
Aside from being able to spot the several special problems that may be present and information is very scant about, the big deal is proper shimming of the trans. Some kind of holding fixture should be used to keep the shafts straight while measurements are made. There is a tool made for this also from Cycle Works.
The clutch should be checked, couple more tools, some of these are found at the corner hardware store
If there is wet oil on the shelf under the trans the the rear main engine oil seal and the cover O-ring from the oil pump should be replaced. Make sure you understand the issue about blocking the crank before removing the flywheel.
That's enough to get you started I think. Do you have a Clymer's or Hayne's Manual?