Hi, I always dry my fibre prints flat on flyscreen racks. Heating fibre while it hangs makes it curl even more than normal in my experience. I rarely have time pressure for producing a final fibre print so overnight drying is fine. If the darkroom is cold or humid I might put an oil space heater on low heat overnight to help. Resin coated paper proof sheets dry hanging from a line over my sink in a short time and don't need any help.
I have
no experience with heated print drying aside from pressing everything with the dry-mount to flatten it, and I'm never under a time constraint to finish prints; thus, my thought to make the negative cabinet a dual-purpose area. My only objection to that plan is the fact that I am known to work on processing dry negatives from the night before, create contact sheets, and then want to get around to processing more negatives later on; rather, I want to work on things while stuff is drying...so if my drying cabinet is taken up with one batch while I'm wanting to use it for the other batch, I'll be right back in the same predicament in which I now find myself.
I too made flyscreen racks that slide under my darkroom ‘sink’ which itself is really just a homemade table with a few shelves. Doesn’t use any additional darkroom floorspace.
If you have a space you put your printing trays on, surely there is an inch or two to be found underneath?
Horizontal seems a more efficient way to go than vertical with drying prints? Especially curly fiber prints.
Building some kind of dedicated device to dry something seems maybe not the most efficient use of resources?

But i live in a reasonably warm climate, maybe prints take a long time to dry where you live?
I've thought about an under-counter area for prints to dry, on a screen rack exactly as mentioned...and under the "sink" would be a good spot. The "sink" - really it's just a big tray that connects to the
actual sink - is the last area that I'll be remodeling, too, so the worst situation I would be in until then is my current makeshift "just stack a few surplus window screens around the place" solution. I hate that solution because I have to shut everything down after just a few prints, but it would work for awhile.
Also, prints do take awhile to dry around here... especially in a small room on the northern side of the house, where the humidity is always a bit higher, and in which there's little air movement. Having them in some kind of partitioned area of their own is really all about keeping the darkroom up and running while they're drying, which lets me spend more time in there working without danger of disturbing them (same with negatives).
If I was smart, I would design a cabinet that's big enough to contain a countertop print dryer and/or drying screens, and then have the option of using either...but I wanted to learn about print dryers anyway, so that'll be fun.