I was looking at the post very early in the F30 release, where the suspension parts of the E90 and F30 were compared with the F30 on the lift. It is interesting to note that the front lower control arm on the F30 (part number 31126852991) is the same shape as that of the E90 (part numbers 31126770849 and 31126770850). However, on the E90 the rear bushing was rubber and on the F30 that bushing is solid. BMW probably did that to give the steering more feel so enthusiasts would not complain about the steering.
What I would consider doing is buying a set of control arms from the E90 and bolting them in. They are listed as $114.04 each from Realoem. It is a very easy job and can be done with hand tools on the driveway. If that solves the issue, you are a happy F30 owner! Or try the E90 M3 control arm (part numbers 31102283577 and 31102283578) which is a little longer and get yourself some extra negative camber in front
and also list at $114.03 from realoem.
There is historical precedent for this. Past BMW's have had steering wheel shimmies and using the control arm from another model solved it (I think the E28 5-series switched to the 7-series arm for example).