There's two of us, and you've worked with both. I've never seen an issue like this one where the gears don't want to slide. Unless I hear a good diagnosis, we'll just replace that whole shaft and gear assembly to be safe.
So the right side 1-3 gears have no play in them. If the left side gear set is meshed on a-c then the 1-3 won’t mesh without major force, or opening the lid and pushing on the gear opposite of where the shift fork applies its leverage. So the 1-3 gear set has one or two gears that have shifted and bound up on the key and shaft and stuck in that crooked position permanently. So if I disengage a-c gear transmission gear set, 1-3 can be engaged easier, but still not the way it should be.
I think it may only be one of the gears inside diameter and key seat have become too large and allowed the gears to slide at an angle, so the only way to get it to move is pushing on both side of the gear so the bore remains linear with the shaft. When I open the snap ring holding them together a little, they move a bit easier, but this may just be due to me applying pressure closer to the center of the gear, so it isn’t pushed at the angle created by the shift fork.
Whatever it is, it possibly can be taken apart and cleaned up, but I do worry about the fact that a gear or two will not be running concentric and perpendicular to the axis of rotation. I don’t believe I will need to purchase the whole assembly anymore. I think the max will be a new gear on the 1-3 idler/trans gear, or gear set. The minimum will be removing them and running a bushing, or something.
Here is a video showing The number 3 gear can be pushed on and one side and the 180 degrees away from the point I push on will move away from the #2 gear it’s seating against with a snap ring.