Hi Scott,
Sorry to hear of your troubles.
Not sure if you have or would be comfortable using one, but a simple measurement of the solenoid with an ohm meter while disconnected from the furnace will reveal volumes. It will reveal if the solenoid is indeed shorted and should be replaced, or whether the problem lies upstream from the solenoid. The reading of the solenoid should be low but not zero. Zero resistance blows fuses. The sizing of the fuse is such that only the solenoid should get power through it.
If there is an intermittent action taking place or a dead short elsewhere, the fuse will blow even if the solenoid is still good.
Talk to a friend or neighbor who is an electronics technician and can use a VOM (volt, ohm, milliammeter). It will be a simple matter for him or her to diagnose your problem. I just would hate to see the solenoid get replaced and still have the problem. Also lubricate it per the manual with WD-40.
Best of luck.
Jerry