http://www.chessvariants.org/unequal.dir/monster.htmlsays 'It's rather like the Maharajah game: it is probably a theoretical win for White but difficult in practice.'
No, Toad, this does not mean its solved.
How do you play as white with the four pawns. After a d7, c7, h7, g7, bg6 or a similar setup for black, I find it very hard for white as black can always sacrifice a minor piece to capture the pawns.
There are tactical combinations involving the move d5-d6;e5-e6 when white pawns are at d5 and e6. This is almost checkmate. Besides, white king can pass by the kingside and use the weakness of the diagonal h5-e8.
A setup with a white king at f4 (g4 or f5) and white pawns at d5 and e5 is very close to win.
but with d6, the the white pawns cannot reach e5 and its hard to attack f7. Also, the queen bishop blocks the f5 point