Hi there this is my first post on this site and I have the answer to SK400 question.
My new box is doing the same as yours with 4th giving the most problem, I have found that its the 4th gear getting tight on the main shaft and some times when the clutch is pressed the gear stops/sticks on the shaft with the teeth not aligned so it will not engage 4th.
If you double clutch and get the gears to spin again it will go into gear, this only happens as the box is warming up and by the time its hot it changes gear very well.
I found going from 3rd to 4th it would not go in, I kept the clutch pressed and rolled to a stop.
There was no way it would go in any gear, I could feel the syncro's trying to slow the main shaft and only when I let the clutch out in neutral to get the gears to spin would it engage gears again.
I don't think there is damage taking place its just very hard to change gear until its up to operating temp.
Good luck.