“My husband and I are moving from Minnesota to Seattle in four months.”
“Corolla’s can’t haul much so adding a trailer hitch to my leased vehicle seemed pointless.”
“We don’t want to spend over a grand shipping anything.”
“I also read briefly that top racks can only withstand about 125 lbs of weight… that obviously won’t be worth it if that’s the case.”
“Basically, we aren’t really wanting to rent a uhal and drive separate, and we dont want to ship anything either.”
Basically, you are moving and taking some stuff, comfortably, and practically without cost, but have eliminated almost the means to do it.
You Need to move, but have Wants that are causing problems.
You’ve painted yourself into a corner.
I think that either you’ll have to loosen your grasp on some more money, cancel the move, or make some other concessions. You’ve got lots of great suggestions here on how to make it happen.