I came to this thread to thank @Gillman for suggesting to solo Marie. Before reading this thread, I was convinced that Ithaqua was virtually impossible. Afterward, I've beaten him 4 times recently, and now I am just aiming for the highest score I can get. I still need to restart from time to time but he is not nearly as difficult as I thought.
I was wasting so much time trying to create the perfect 4-player team but the fact that you can't share items makes that ineffective. The key to soloing Marie is choosing those early adventures very carefully. You need to succeed to have trophies (money) to use her ability.
As others said, prioritize locked dice, then midnight effects, then monsters. Try to open as many Other Worlds as you can and always save the Other World action just before midnight (many times you will complete an adventure and then an adventure with midnight effects pops up before you can do anything about it).
I tend to have 20 supplies at the minimum, but I found that I have too many supplies at the end, and win with 10 or so remaining (however, I've had a random effect that removed -13 supplies, so keep that in mind). Again, I am aiming for high scores (8968 is my best) so my supply count is probably too high.
When you travel to the second area, do your best to avoid winter effects (unless you have to) and adventures that take your items (unless you don't have that type of item in the first place). Again, open, as many Other Worlds as possible. Save your ability for when it is only absolutely necessary and if you play long enough, you will be going up against Ithaqua with 20+ trophies. Avoid healing yourself, unless it is absolutely necessary. I tend to gamble my damage until I am nearly dead in both Sanity/Stamina to make a healing turn (which costs 4) as valuable as possible. If you are regularly opening Other Worlds, and choosing adventures carefully, I've won games where there were 7 or 8 packs of wolves near the end and it didn't matter.
Ithaqua is not that bad if you solo (or perhaps a team of 2).