Hello Andy
I hope the backplate is big enough to fit the chuck!
it's normal to turn the backplate register so that it fits the collet chuck very closely. What is most important is that the front face of the backplate, where the chuck fits, is skimmed absolutely flat to provide an accurate location to avoid wobble. Having achieved a good fit on diameter, you then need to drill and tap one or other of the items to hold them together; using the one to spot the holes in the other is the usual way. Fit the thing together and do the screws up. Job done. In theory…
If the PCD of the existing holes in backplate and chuck don't agree, then you'll have to choose a suitable orientation for them to get some metal in the appropriate positions.
However, it's very likely, looking at your backplate, that the turned register on your backplate could be smaller than the female recess in the chuck. (If it isn't, just turn it to a good fit as above.) It can still be used if it's too small.
Having got the bits together and done up the screws, clock the tapered bore of the chuck with a good clock gauge. Unless you're really lucky it will probably be a little bit out. It's a case then of dismantling, skimming off a small bit on the diameter of the backplate register and re-assembling with the screws gently nipped up. Clock up the bore again and use a soft hammer to bop the chuck true to the clock gauge. This may take some time (and bops) and may even involve skimming off a bit more of the register diameter, but persevere and you'll get there. Tighten up the screws a bit more and re-check with the clock gauge – it may need further bopping. You should be able to get it to virtually zero runout.
Then, before you do anything else, I would then drill two little dimples, one in the backplate adjacent to a Camlock pin, and another on the lathe spindle close by so that you can re-fit it in the same orientation. Fill both with red paint. (I've done that on my Boxford 280 and all my chucks are marked.)
Hope that helps!