Mark; Look at the plate carefully. Thee should be a "step" or raised ring on the plate. Measure this diameter very accurately. It should also have bolt holes in it. Either 3 or 4.
You can get an face plate with the ER32 collet chuck on the front. You may have to drill the front face plate. Bolt the plate to the back plate. True the collet chuck so it is accurately aligned. Check Chronos.uk for chuck face plates.
Measuring and truing that step is critical - depending on how good a job in making that plate on the end of your spindle. I hope you have a good dial indicator that you can use to true it to less than .0005
That will be the start of any runout you compound with the collet and chuck themselves. If you can't do that or it's impractical then leave enough play in the chuck mount so you can true the inside taper of the chuck. You may have to do that anyway. All that is standard procedure for a lot of chuck switching in the industry. If your chuck taper is good you can complement that with good quality collets that have a TIR of less than .0003 or .0004 --- It's all money
Your lathe doc didn't seem to spec any spindle runout so my guess is it's probably about .0005 or a little less if you're lucky. Be lucky!
(Remember the symbol for taper is "tau") :biggrin:
You get all that done and I think you'll be very pleased with the result.
Attached is a picture of an ER40 chuck setup on one of my machines. It has 4 axes of adjustment for precise alignment.
Cheers,
Rich