So here it is: the BBK
All your nice words about my last experiment gave me the drive to get it done, thank you all for that!
I knew I had a "butterfly comb" laying around somewhere.
I cut off the comb part of it with an angle grinder and then cut the knife blade to the right size.
I did not remove the handles though and that ended up biting me in the ass...
Using a magnet, I positioned the blade against and in line with the stub left from the comb and proceeded to stick weld them together.
I was dreading that moment as I'm not good with welding and even worse when it comes to thin-ish material, but it went pretty smoothly and I'm happy how it turned out!
I then went on to grinding. I tried removing the handles but only one came off, the heat from the welding must have something to do with that...

Anyways, the hard part was behind me and all that was left was to grind, sand and polish it as well as my impatient self was willing to.
And there it was:

In all its splendor

The

Butter

Fly

Butter

Knife
I'm adding a parallel comment rather than editing my existing comment because that adds one to the count and that sort of thing probably boosts engagement^tm^.
It may be too late for this now if you've significantly warped either of the pivot screws. But the trick for getting these headless screws undone on a balisong is to crank them with the knife latched. The idea is that the force going down the handles will bind the sides of the screw posts against their holes in the blade and/or the handle, holding the female end tightly enough that you can undo the male end. This works frequently enough that I'll classify it as "often."
You can perform a similar trick on a single pivoted knife, i.e. a normal one, by clamping it in two blocks of wood in a vise such that you're pressing down on the spine of the blade right over the pivot.
Thanks for the tip! I was wondering how one is supposed to unscrew those and this makes a lot of sense.
I think on of the screws is warped though, I gave the headless one a slit to be able to fit a flathead screwdriver in there and it didn't help.
I hope I will remember this next time I disassemble a knife.