I wish I could help.
But it’s just too complicated

If you liked the king bed and can maneuver the mattress up the stairs, I would stick with that. The split box spring shouldn’t be an issue as long as the mattress is rotated every three months, flipped every six months, and is of acceptable quality. It should last a min. of 10 years and more likely longer.

Another option is to find someone who can build a frame and/or box spring. If it’s the former, a piece of plywood or two can be placed on it to support the mattress.

I’ve slept one year, 5 years ago, without a frame. It wasn’t the end of the world.

4×8 sheet of plywood. Or two of them.

Mattress on top of plywood.

If you can’t fit the box spring, would you be able to fit a queen size platform bed up the stairs?

I think slat rolls need more of an enclosed frame that doesn’t have open ends like there are on metal slide-together-types that are meant to be used with box springs.

I would choose between bunkie board or split box springs—depending on how vigorously you plan on using it. ;)

Ask a moving expert how to get the bed you choose to your room.

My last few mattresses have been on slats with no issues (Ikea slats, if that matters, on Ikea beds). I’ve also used plywood – don’t remember if that was on top of slats or not.

I don’t think I’ve used box springs in about 20 years.

How wide is the bedroom window?
Hoist it up to that window perhaps.
I have seen huge Pianos moved in that way.
( depends on the window size and if the windows can be taken out and placed back in?)

An other option is to sell that bed and get a “Casper” bed ( foam)?

https://www.amazon.com/s?k=Casper+bed&ref=nb_sb_noss_2

A year or two back I ran into a failed box spring and support frame (queen size) and was faced with replacing the entire ensemble (bed is 25 years old). I’m a retired pensioner in my 70th year so I could not justify a new $1,000–2,000 bed. What to do?
After months of research/procrastinating I settled with a “Zinus Smartbase Bed”. Threw out the box spring and it’s base; and have slept like a king since. The smartbase cost less than $100 and I put it together with no tools (all wing nut connections and fastenings). It’s capacity of 2400 pounds holds me perfectly. The shipping box is about the size of ½ of a single mattress.
Check it out at link
I tried to cover everything, but if something seems to be missing, just ask.