I agree to buy individual parts and custom fabricate the unit. We have a large 14" hydraulic extruder in our studio that is a one-off piece of equipment. If I recall correct, it was built by someone at Univ. of Minnesota.
Ours accepts a 16" square die plate, with an approx 14" extrusion limit. It has a hydraulic cylinder for the main ram, which as control valves for the hydraulic pressure and up/down stroke. I can stop it during mid-stroke, I can also change the speed during mid-stroke...it also tilts into horizontal position AND has a 2nd ram hidden inside the base to make it taller for extruding longer forms in vertical orientation. I can try to take some pics, but in my honest opinion this thing has some major design flaws that I would definitely change if I were to build one myself (the issues mainly are due to the capability of going into horizontal position and being able to change vertical height - it just needs some major improvements for safety). We have the Bailey pneumatic as well, I would likely share some of those design concepts if/when I finally decide to chop into this thing.
The original dies we got with our extruder were mainly for extruding slabs/tiles, but we've since made many of our own. The problem with this is that when you have a LOT of hydraulic pressure + a large diameter die plate, you can very easily snap dies in half (depending on the shape, since certain shapes restrict too much clay and create too much pressure behind it). Many of the dies with smaller apertures have to be double thick matieral (3/4" plywood) or made of something else, like steel.