We also don't have an easy way to pick up a fridge (it won't fit in our car) and delivery dates at other companies are just as far out.
So, having cancelled we're now just kind of SOL.
We may end up getting bailed out by a friend with a trailer, we'll see.
But I'm honestly as concerned about the fact that their support reps seemed legitimately scared when they couldn't help us and it was clear we were unsatisfied with what they could offer us as I am about our lack of a fridge.
Support people shouldn't be scared like that. It's not on them. It's on the company.
Later, but not too much later, sue BB in small claims for the difference between the price they charged and what you ended up paying. It doesn't hurt to ask for some compensation for your time, though you're less likely to get that. The point is, you are most likely entitled to be made whole for any increased expense you incurred to get a fridge on your required timeframe, as a result of BB's breach of contract (yes, you had a contract with them - you have a contract every single time you purchase something, whether it's written or no).
Cancel the order, go the store, get a new fridge. It's honestly not that difficult.