Since you have the 60Hz signal without the fuse that means that the stator is good.
Replacing a stator is not a task for the faint of heart. One practically has to dismantle the entire front of the generator just to get to the point where he can get to the stator. That is, if he can even find a replacement stator...
So, the fuse has saved the day.
The fuses in your picture are the right rating and physical size, but I can't tell from the picture whether or not it is a time delay fuse. You might want to google that part number to see if it is slow blow/ time delay or not. Since it blows 'immediately' and not in a few seconds it is worth a check.
The first thing I'd do is to make sure I had several (~5-6) of the correct fuses.
Since moving it 'seems' to have caused the problem then the first thing I'd do is to remove the regulator and give it the sniff test. Does it smell like it has cooked? Probably not. Next thing I'd do is to make sure that the ground for the regulator is good. One of the wires is connected to a ground terminal on the inside of the unit. Remove those wires and clean up the connection.
If there is any corrosion on any of the terminals on the regulator clean them up and re-install the regulator and test. It is possible that there was a marginal connection on the regulator / ground, and moving the unit aggravated that connection.
Unlikely, but worth a shot.
If you have a known good generator, or known good regulator, swapping out the regulator would tell you a lot.
There are other areas where movement could cause a problem.
WITH THE BATTERY GROUND DISCONNECTED
You can remove the front cover of the generator stator. Inside there is a small terminal strip which could have developed a marginal connection. Remove the wires to the strip one at a time, clean up the tabs and re- install. That strip is not easy to reach, but there are only a couple of wires to fool with.
In general, if a component didn't fail during the move you are probably looking at a marginal connection. If you use the wiring diagram you can remove plugs from the jacks and plug them back in on any of the circuits that connect to the regulator.
All that said, assuming you have the right fuse, my money is on a bad regulator or a bad connection on that little terminal strip in the front of the stator.....
good luck
z