Hi Emily
You have picked a really interesting project. I work on breeding Canna as a crop, and it is a fairly close relative of Musa. I am in the subtropics, so my work is a lot easier in some ways, but being stuck behind Australias quarantine restrictions means I could only dream of working with all those amazing banana species.
My research and experience confirms that pollen for this whole side of the plant family tree is almost impossible to store for any useful length of time. Banana breeding is limited by this factor too. I’m worried you may have a hard time getting two or more species to mature at the same time to allow crossing, given your challenging conditions. Even if you get species going and flowering, getting the timing lined up could be the trickiest part (I used up two years trying to coordinate the Cannas I needed to cross). Have you considered seeking out a collaborator who lives in a state where making the initial hybrids might be easier? Then you would be starting with high enough grex diversity to have more of a fighting chance.
The other thing I would suggest is to consider what agricultural ecosystem role you want the banana to serve in your system. Someone could probably select mangos to produce in Alaska if they lived for 1000 years, or they could start with something that is already most of the way adapted for local conditions. Enthusiasm is essential, but will only keep going if you get results sooner or later.
One alternative would be to consider breeding fruiting bromeliads. Pineapple isn’t the only species with edible fruit, though it could contribute superior genetics. There are two fairly dry hardy Bromelia species, and pretty much the whole family can be used to make fertile hybrids. Some are quite cold/dry hardy as well like Puya and Dyckia. Agave also comes to mind as an option nobody is breeding (for syrup production). Apparently Agave pollen can be stored long term too (https://www.researchgate.net/publication/228494439_Simple_methods_for_in_vitro_pollen_germination_and_pollen_preservation_of_selected_species_of_the_genus_Agave)
If I was you, I would get as many potentially interesting species you might consider breeding into the ground in your growing space asap to assess how they like your conditions. Microclimate and variations in soil are huge factors as to what will grow well. Can you access banana suckers of any the species you are considering just to gauge their performance? (Or are you sticking to seed to reduce disease risk?). You might discover you have superb soil for musk melons or something else you haven’t seriously considered yet. Or, if you are genuinely obsessed with Musa this kind of field trial might inspire you to relocate to a location where they will grow without too many hassles.