What is the history of the vehicle? Have you owned it since new? Has the a/c compressor ever been replaced or is there any aftermarket electronics on the vehicle?
Any link I've tried for Nissan OEM parts says the a/c auto amp is no longer available. I do see them on eBay, but it looks like the part numbers are all over the place between the 2013-2020 model years.
I’m the only owner since buying it new in 2017. Never had any issues with the A/C or climate controls. I don’t have much options but to just fork over $1400 and hope that will fix the issues once and for all. It’s been torture without A/C this summer.
I would dig out your a/c auto amp to get it's part number, then search for a new/used one online if I could find one reasonably enough to swap out and see if it makes a difference. You'd have to search, but I think the a/c auto amp is either behind the radio or in the console somewhere. Either is not too difficult to access. Lots of info online about that.
These systems usually default to w/s defrost and floor mode as a fail safe, but who knows with this particular system. In terms of the hot/cold blend door. I wonder if there's a way to manually actuate that so you have some heat in the meantime.
I'd lean towards finding someone who is really good at doing this type of diag work and have them see if they can solve this. It would be interesting if this was all a/c auto amp related.