Hi there . Maybe try using an independent 4 jaw lathe chuck with removable steel jaws say, 12"-16" dia. You could fabricate a plate to mount it on & attach it to a turning device similar to what the pic shows, or what you already have. You could tailor make a set of end effectors that could either be welded to the actual jaws of the chuck, or preferably machine the bases of them to fit in the groove of the jaw carrier that rides in the scroll of the chuck. The jaws are generally held on to the carrier by two bolts. Then you could fashion the end effectors coming off the jaws to fit several different sizes of pipe. They could be L or C shaped, able to open & close on the part to be fixured. The adjustment would come from being able to move all 4 jaws independently of one another & you could set it up however you wanted, using only as many of the jaws as you needed to hold the part in place. Then, use a clamp around the back, or whatever you needed to keep the elbow with the fitting on it secure. You would only need to make sure that you align the jaws up at the same time to keep the part on the CL of the chuck's axis.
If you put some time into the end effectors & made them very well & robust, a clamp may not even be needed. You could even use insert pieces made from actual pieces of the same size elbow(s) you intend to fixture. Then just use countersunk screws with hex heads to hold them in place inside the end effectors. It may give a real nice hold on the workpiece. When you're talking about a "universal" type of fixture, sure it probably wouldn't be as fast as using a dedicated jig to hold a specific part, but if you're not doing production work on several pieces all day, it won't really matter. I'm not a pipe guy, nor am I an engineer with a degree from a prestigious technical university, but I worked in the automotive manufacturing industry for about 5 years & looked at a LOT of fixturing on the robots I fed all night. Frankly, industrial structures & fixturing fascinates me. They could build an end effector, or gripping unit on the end of that robot arm to pick up or hold just about anything!
Really, it looks like a pretty straightforward setup in the pic. Just that theirs is non-adjustable. And, it's not like you need to hold it with a terrific amount of force, as if you were machining it. Just enough to keep it set in the fixture so you can spin it as you weld on it. Are you holding the attaching piece of pipe on a roller or jig to tack it up in position too? Just wondered. You can pick up used chucks pretty cheap & even get thinner, table mount ones that aren't so beefy like one that mounts on an actual lathe if you look around. The only drawback would be that the chuck would be heavy. But, if you're looking to use this thing for a long time, it may be worth sinking some time into making it right. I don't know if that is what you are looking for as far an an idea goes, but it's just a thought....... Good luck on it! S.W.