First thing you want to do before you do anything else..........wash that critter!
Working on a dirty Ody sucks, the cleaner the better.
According to the picture in the manual, the valve side of the three way fuel valve should be on the tank return side. This is set up so that once the fuel bowl is full, it will cause the valve to open and allow the fuel to return to the top of the tank. By the looks of your picture, your Dad has it set up correctly.
1.) Make sure your fuel filter is working properly and check to make sure in fact that the fuel shut off valve is working properly. Just because it is new, doesn't mean that there isn't something wrong in that area. Pull the carburetor off and then pull the bowl off. Blow air through the carburetor fuel line. While doing this, move the floats up and see if it prevents you from blowing air in through the fuel line. If you can still blow air through the valve when the floats have been pushed up then BINGO, there's your problem.
2.)
Engine cradle mounts. The FL250 has a funny tripod cradle system for the Engine to mount to the frame. I have had several of these fail on me. When they do, it will cause the Engine to shake
ALOT It is usually one of the front two which fail, however, make sure you check all three. A failed mount can cause the floats to vibrate excessively and can cause the carburetor to overflow.
3.) Double and triple check your float height adjustment. When the floats are set too high, the fuel level will be too high and will cause carburetor overflow.
4.) Check your timing. As mentioned before, improperly set timing can cause Engine shake. Think about this, ever been in a car that didn't runs quite right and felt it shake the entire car?
Rand