No way i would have let the bike do what it wanted, i would have crashed, it was still wobbling when i came out of the turn going straight, it didnt stop until i reached 20mph, needless to say I'm done thinking i'm riding my CBR 1000 i gave up two years ago. Live and learn.
The different stabilizer links can help.
Do a search on eBay for "Harley Progressive link" for one that works well at a reasonable price ........ 'and' probably slow down some.
Steering head bearing needs checked for proper adjustment. Wouldn't hurt to grease it up also. Make sure both tires are at the proper inflation and also check to make sure the back of the bike is not overloaded. The stabilizer link would no doubt help out.
What year Street Glide do you have? You state it's your front tire that wobbled--all the way down to 20 mph. That would be different than the weave many experienced in curves on the tour models with the old frame. The stabilizers you all mention are only for the old frame.
Check fork oil, head bearings, tire pressure and balance to start.
It's an 08, tire pressure is good, fork oil was just changed when the Yaffe bars were installed. Someone mentioned weight on the rear end, my bags were full, that may have had something to do with it. I'm bringing it down to have the bearings checked.