IMHO, if you cant ride it no hands without it getting the wobbles...look for a better designed frame. theyre meant to be enjoyable to ride, not a struggle, and not a pant-soiling experience either!
rake, trail, steering tube angle, wheelbase, they all interact and play a part. increase rake, reduce trail, but by increasing the steering angle, trail returns...but then the wheelbase is lengthened and and and ad nauseum.
quadratic functions, anyone? with no guarantee that the answer is actually correct...
bmx forks on an old 20" cruiser made it rather sketchy. reduced the rake, which increased the trail. already a rather steep steering tube. well.... im glad the bearings have flogged out cus now i have to cut the steering tube out and replace it
and im not currently riding it, another godsend
had a really unnerving habit of just falling out from under... and was definitely a keep both hands on at all times type bike... id have stuck with the orig forks but they had those silly lil 8mm hole, squashed tube dropouts typical of the era... just a tad flimsy.
one exception... my old postie bike. that thing would shake violently no hands, but would still hold a perfect line, even through corners. freaks out the people driving in front when what appears to be a motorcycle doing death wobbles comes up behind them
(the headlight waves madly side to side along with the front wheel)
by violent i mean it would hit the stops HARD. faster oscillations than was physically possible if you tried it yourself. around about 60 degrees to either side... never had anything else capable of doing that!
that spring would do doodly squat. its barely in tension where it is, is only a light gage spring, and would require a LOT of rotation before it added appreciable tension. really requires a long arm on the fork part to increase the movement.
worst case scenario, get a REAL damper off a motorbike. a damper dampens oscillations. a spring springs and bounces...
personally... i cant ride a moto with a steering damper. feels all wrong, like the bearings have been overtightened...