Robin, to be honest I don’t think that’s a job for a cheap drilling machine, unless you have a means to position the workpiece exactly (eg. a x-y table). I also don’t think that a Jacobs chuck is much better than a Röhm, at least I suppose it is not a chuck salvaged from an old hand drill?
But to give you some constructive ideas:
– use a center drill, best a so-called NC center drill (the Slocombe (?) drills are for doing centers to put a lathe center in)
– use a self-centering drill, either a 4-facet or one with a split point. These have no chisel edge which can wander around on a flat surface, but a really sharp point in the center.
– doing it in the lathe would be a good idea also; either by first centering it in a 4-jaw (and then only releasing one jaw to change the workpiece), or mounting it with suitable shims and stops on the cross-slide.
I hope this can be helpful
Greetings, Hansrudolf