With the 101 pure copper tube I used (because it is slightly more 'efficient') I couldn't find thinwall at a decent price, so bend radius pinch can be an issue. With thinwall 12x tube it really isn't necessary to use a filler. Half hard tube will bend without collapsing easier than fully annealed tube, just use a cheap bending tool available at your local hobby shop or on the net-
https://www.towerhobbies.com/cgi-bi...MIr5Sar6rV4QIVzZyzCh0DYA5xEAQYAiABEgJmTfD_BwE
You can make some pretty tight radius bends with this, it do take some practice though.
Square or D profile tube is supposed to even more efficient, I've wanted to make a press die for turning round to square for quite awhile now. It ain't difficult, but you'd need to fill it during the bending process, because that WILL kink or collapse.
Not sure what the "12x tube" is, I just got a piece about 3 feet long that I am not sure if it's soft or hard this is why I want to use filler just because it's so simple to do it, why take chances, fill it with water or fine sand I got, seal the ends and band away. I got a lathe so I can machine any mandrel I want, I can even make the round "thread" in delrin rod for tube to follow exact spacing but it's probably not necessary. Forming coil should be simple too, chuck the mandrel, lock the spindle, rotate, bend, repeat. Regarding bending tool, I don't really see the need for it. I've read the link you sent on coil design I've read it and saved it in my favorites but even though it was pretty good information overall it did little to help in our quest for better coil, the breakthrough I saw was Fluxeon ferrite with litz wire coil as well as interesting variation they did for Giraud, it looks like ferrite oring that had opening cut out and simply wire wrapped. Once I build the normal coil I will play around with that. https://fluxeon.com/product/annie-flux-concentrator-coil/
Regarding the square or D profile tubing, I have small milling machine and small hydraulic press and you stirred my brain, I should be able to make this fairly easy. My guess that D shape would bend more naturally than square tube I could probably even make it out of aluminum, square die would be easier to make. You can share your idea how you envision the forming die.