It's possible the shaft is dry and needs lubricated. I usually take the shaft/cable out of the housing and use a good lithium grease to lube the shaft/cable. Also i normally turn the shaft/cable end for end when i lube them. I lube mine annually.

Try running the engine without the shaft assy.
That will isolate the vibe.
Bill

Thanks bill and nod. Will do removal/inspection/lube/etc regarding shaft/cable here in short order. 2 follow-ups if you please:

1) When you say -end for end- you mean flip/invert it and reinstall, right? A fix that assumes problem area is not exactly at the midpoint :-) ?
2) Could/should such a failure show up ONLY after a warm-up period? That is to say, would you expect it to go haywire sooner than later...or later than sooner? Thanks dudes!

Ugly Gringo

The Drive Cable rests in a nylon? tube and should not cause a vibe like you describe Reversing the cable should help spread the lube and end wear more evenly.
I doubt a broken fin on the rotor would make that big a vibe, but you might check. Also look at the spool for uneven string blob.I suspect the vibe must be at the bottom end.
Does the vibe start after the head begins to trim?

I have any part you might need...New or Used.