I think they are now quite well known since PF made that youtube video, and they are made for over a century in Germany. I am very happy with my vintage Heuer and the brand new ones are exactly the same.
The HEUER bench vice with replaceable jaw - the best clamping tool for the professional. Made in Germany, steel-forged, guaranteed unbreakable, top in tests!
www.heuer.de
For custom jaws, you would need to go for the model with replaceable jaws. The nice thing is, they screw on from the back, not through the jaw, so the whole surface is usable. If you do not mind through-holes for the screws, the same jaws can be used on both sides or even on all four sides (I guess it can be done with regular vises too, but you typically need to go deep to hide the allen head, here it's just a threaded hole).
They are made of forged steel and are extremely versatile and will handle stuff like actual forging on them (you don't want to do that with a regular cast iron vise). At the same time, the screw in the centre pinches the "X" guides so you can take out any slop, making them also fairly high precision. And being forged steel, they get away with using a bit less material, leaving you more space around what you're working.
Particularly, the width of the guide and the spindle is very narrow relative to the width of the jaws. This is usually not so on cast iron vises. Here, a lot of the space "under the jaws" is unoccupied, so you can clamp in tall objects even like bicycle frames or shocks (especially the larger sized Heuer vises). Since the spindle is not inside the guide, but rather in between the guide and the jaws, tightning it down also distributes forces better (the spindles inside the guide are often a little bit underneath the guide, which means the clamping force is bending and cracking the moving jaw off of the guide - on the heuer, the clamping force is formed in the middle, above the guide, so it is a more favourable distribution and more of the force goes into what you're clamping instead of bending the guide).
They've got this funny ad on their site:
I think most people on Garagejournal can relate to that!
You can also get all sorts of special supports for them, like a height adjustable lift-arm for the table, a collapsable lift-arm so it hides under the table when not in use, a rotary table, and even a lift stand you place on the ground and use without a table.
I bought a 140mm forged jaw version for 180€ about a year ago for the company (means it is without VAT here in Europe, otherwise it would be about 22% more if bought privately). I read the prices in the US are sadly much higher.