I started playing this about a week ago, and didn't really consider solo-play with more than one character at first. After some bumps and bruises, I started to get an idea of which characters worked well by themselves. As most of the bane cards in any location deck are monsters/henchmen/villains with combat checks, I found that characters who were more likely to pass those checks worked best for me. They could still have problems with a barrier or difficult-to-beat monster (I learned to really, really hate Sirens), but otherwise, it was pretty easy. My best characters for that were Valeros, Merisiel, and Harsk.
Playing one character meant that I didn't ever have to worry about the time running out. Only a combination of having the villain/henchmen be on the bottom of each deck and some bad die rolls would enable the blessings deck to run out (and assuming I never once used a card's power to continue exploring). Of course, playing one character means that you have no shot to temporarily close a location when a villain escapes, but that actually worked to my advantage. I learned to look at the locations and see what the closing requirements were, then made sure that the most difficult (or detrimental) location to close would be the last explored, since defeating a villain automatically closes the location. The villains I'd encountered so far all seemed pretty easy to beat. I know that they will get harder as things go along, but I'll cross that bridge when I come to it.
One place that I did get hurt at alot was that Shrine of Lamashtu that showed up in Black Fang's Dungeon. One time playing it with Harsk, I found Black Fang in the first location explored. So when he escaped, I had to get a blessing and shuffle it and Black Fang and then shuffle a card each into the two remaining decks. Yep, I found Black Fang in the second location and chased him to the last one (the Shrine) so I now had 4 blessings in there. I hit three of them on three consecutive draws (for 6 total points of damage). Ouch. But fortunately for me I had only discarded 3 cards at that point (and 5 in my hand made 8) and I had 7 cards left in my deck. After all the blessing damage I still had 3 cards in the deck when I found Black Fang at last (for the last time) and ended the scenario.
I did play the first scenario of Burnt Offerings with each of the three solo, and it was a little more difficult (but only a tiny bit). However, looking at the next one, I'm actually a little worried. Fighting monsters is not the focus, but gathering allies instead. Most of the allies I've seen require checks I'm not confident that these three will make. In most cases the die rolled will be a d6, so careful use of blessings to add extra dice to the checks will be very important. Moreso, because I might have to team them all together to increase my chances of successful ally recruitment, which means I might find myself having to burn blessings to continue exploring locations before the timer runs out. Should be interesting...