What is involved with finishing the mounting features of back plates and chucks?
Basically, you find a back plate that fits your spindle like the one RJ found on ebay. Then you find a chuck to match the size of the back plate. Depending on where the mounting holes are drilled in the chuck, this will be either a 5 or 6" chuck. You need to mount the back plate to your spindle and then machine the face of the plate to match the features found in the back of the chuck you need to mount. Most commonly, there will be a recessed area in back of the chuck so you need to machine a snout on the back plate that will fit inside this hole. Note that once you start to machine the plate, you do NOT remove it from the spindle until you're done. This assures that any machining you do will be as accurate as your spindle.
There are several schools of thought about the fit of the snout in this hole. Some feel you need a press fit and will make the snout (called a register) half a thou or so larger than the hole. This allows the chuck to be very accurately located and assures that it will not move around under load. Others feel that you should have some give in the hole and I happen to fall into this camp. I prefer to make the register a few thou smaller than the hole so I can indicate the chuck into near perfect alignment before locking it down with the locking bolts. Samchully, a maker of very high quality chucks, recommends this method and I've found it to work rather well.
Once you make the register/snout thing, you face out to flatten the remainder of the back plate and then mount the chuck. You then transfer the mounting hole locations that are already present in the chuck to the back plate with transfer punches and then drill and tap the back plate for your locking bolts. Then you bolt that sucker down and you have a new lathe chuck.
It is wise to mark each of the three pinions (a Sharpie works) and then insert a short piece of ground rod into the chuck and lock it down. Measure the run out of the rod with an indicator, then loosen the chuck and re-tighten with the next marked pinion. One of the three pinions will produce the least amount of run out. If you left some room in fitting the chuck to the plate, you can loosen the locking bolts to minimize run out and then lock it down for good. Re-check to be sure you know which is the most accurate pinion and then put a witness mark somewhere so you know which pinion it is. Also mark the spindle and back plate so you know the most accurate mounting orientation. When you remove and reinstall the chuck, align the marks. When you mount work in the chuck, use the marked pinion only and do not tighten the chuck with the other pinions. This will ensure that your chuck is as accurate as it can be.
There are videos galore on how to do this. Learning how to do this allows you to use any plain back chuck on your asian lathe so it is a skill well worth learning. There are many high quality chucks on ebay that you can buy for a song IF you know how to mount them.
EDIT: I highly recommend that when you find a source for your back plate and find that it fits your spindle well, buy at least two. If you mess one up, you have a back up. If you get the first one right, you have another for another chuck. If you ever buy another lathe, get one with a D1 camlock spindle. Almost every maker of high end chucks make them to fit a D1 spindle. It will likely be more accurate and it obviously saves you from the headache of mounting a chuck to a back plate.