Looking for a decent solo variant for the game.  Any suggetions?

Just off the top of my head and completely untested I'd say try starting with the Crisis countdown at like 20 or so.  Play as normal from there.

Well, one variant I tried was starting as normal, treating areas as if there were 2 players (start with 2 in play, limit is 4), and if an encounter card would be discarded because it's too high level, a replacement is drawn (and discarded and redrawn as necessary until you get one that can be used).

First problem I noticed was being unable to kill anything.  One character has a very tough time against just about every monster.  So perhaps that part isn't too good.

Another idea, though, is perhaps change the rules for combat: if a fight is lost, the party must make a speed check against the enemy's combat ability.  Failure means that one character dies, in addition to any other bad things that happen as a result (so losing any combat by at least 5 means you lose one character automatically, and may lose a second).

I may have to make some houserules for the "only against players" cards as well...

Like Robosheep said. Play again with an active crisis timer 20 is what I have been doing as well, but to further aid I would suggest removing the pvp type cards from the deck. I have been doing challenge runs solo by mixing the BGaE and SoO character, encounter and advantage cards. Then I removed from the advantage cards any thing that seemed more or less pvp related. I also went though the advantage cards and removed traps and the character card that detects traps. Then I play the game only using BGaE lands and missions. Not as fun as with another player or two, but its great for killing some time.