Furace fuse blows when Aprilaire humdifier is turned on above 35%
The solenoid shouldn't blow the fuse, unless there is a short in it. It's not like a motor that has high locked rotor current, which could blow a fuse if the rotor was frozen. If the coil of a solenoid energizes, it doesn't matter if the plunger moves or not (electrically speaking).

I'd check the resistance of the coil, versus the specifications for the solenoid. This should tell you if there is a short.  Depending on the price of a new solenoid, I might just replace it if it's in as bad a shape as you describe.

The other thing to check, would be the humidistat. 

I'm not sure why you'd see a fuse blow at one humidity level, and not another. I'm guessing the unit didn't kick on until it was set above 35%, so the problem may or may not depend on the setting.