Short of doing new Dungeon Master mods of SOH, I can think of two ways to play SOH solo. Both involve a trip to your stationary store.
1: Buy some big postits. Turn the GM book upside down. Cover the maps, except the stairs down, the first room and the portals, for each level. Cover all on the right page describing the rooms. Since it's upside down, this makes it tough to absorb much. Go thru all levels covering things, making it even harder to remember much. As you go thru rooms during play, adjust the postits (upside down) for room description, and uncover only the room you're in. Then read it, but randomize anything involving a specific board square or searching task, then use enemy AI. Decide on which exit you'll use, turn upside down, move postits to reveal the next room, jiggle postits to reveal its description, turn it right side up, and continue. Funky but it should work.
2. Buy some labels and cheap playing cards. Keep the jokers. SOH has 54 rooms, so write on the label a note with the room number and level name and stick one to each card. Mix with all ST cards if desired. Draw a card, and randomize its internal portal connections based on a compass orierntation, perhaps roll 3d6 to determine the number of portals, such as (assuming a south entry) 1=west portal, 2=no west portal, 3=north portal, 4=no north portal, 5=east portal, 6=no east portal. If you don't have 3d6 worth, roll again. Draw and place a tile based on each card drawn. Find book references and stock with defined enemies or traps, etc. as defined. You might want to add a random chance of gold in ST tiles since that's new. This doesn't give the SOH experience but lets you build random dungeons in the spirit of the old WQ system.
You can also recreate the old WQ random enemies system to make things more unpredictable. Then, make a 2d6 table for all the bad guys you got (the first dice=tens, second dice=numbers approach, to give from 11-66 options, and fill out the table with the dudes you have minis for and that have rules, including exotic adversaries. Roll 2D6 when you enter a random room, and have at it!
I am sure this could also be easily coded, but until then...