You can make the backplate in situ.

1. Get a piece of steel (preferably) or ali (ok for small chucks or lightweight work) round approx the right outer dia (3"/75mm) and 20-25mm thick (have a look how current chuck is mounted).
2. mark out and drill the holes for the spindle side then bolt it on the spinndle in place of the chuck. WHat I've done in the past is actually use longer bolts and bolt through the existing backplate so you have it nearer the tool as some lathes wont reach the backplate otherwise (or not without a lot of tool overhang and you dont want that).
3. Then you bring the new backplate to size on the external circumference
4. Machine accurately the step to fit the chuck recess, testing it regularly until its a tight twist-on fit.
5. finally you use the tool to score a circle at the right diameter for the holes and the x-slide to mark them at 90deg intervals on the circle.
6. remove backplate, drill holes and you're done.

If you can't get rounds, use a square bit of plate do step 2 and use a long ended parting tool to cut into the face of the plate larger than the finished diameter of the outside, then proceed from step 3 above