Starter/solenoid prob?

1993 Explorer XLT starter/solenoid problem? I have a 1993 Ford Explorer XLT 4.0L with automatic transmission. The odomoter reads approx. 104k miles, although the vehicle title states it is void due to the vehicle having been wrecked and a different motor was installed. There is a heavy-duty toggle switch for the starter with 10 gauge wiring. Just recently, the car became very difficult to start and keep running. I cleaned and replaced battery terminals and the battery is less than 1 yr. old. When it starts, it runs fine for about 30-60 seconds then begins sputtering and dies, then is impossible to start for a period of time. I noticed the smell of burning wire coming from the starter/solenoid, and the solenoid was extremely hot when i got underneath the car to check it out. Sometimes after an hour or two it will almost start again, but usually fails. Had the battery recharged and checked plus the alternator checked and both were ok, according to Auto Zone.
Was planning a 600-mile trip to visit children this Saturday...any helpful tips or advice would be greatly appreciated, I'm desperate!!