The last time I tried one of the ultimates, with all squads at or above the 38K mark, I only barely got through and that is with a very strong helper (stronger than me by far) as the sole survivors. Your first squad is stronger than mine even now though, so with that and a strong helper you might get somewhere but I expect your 2nd-4th squads to not make it unless they never encounter pests.

I find the equip-unequip to refresh the list works but I have a specific way I do it (hit remove from, select, then add, the item, then select again, then home). Some other ways of doing that didn't seem to have the same outcome.