New (ooold) road bike shimmies...?

It's my friends dads old 27" tourer given to me, everything (brakes, shifters, steering) works great until about 20 mph- above which I have to pinch the tt and have my hands off of the tops to keep her steady. The front was a little out of true and I wanted sealed hubs anyways, so she got new wheels laced at my lbs... Still wobbling. Eyeballing from the top of the stem down along the steer line seems to have at least two inches of trail and the fork legs setting back a smidge (kind of like old track-racing forks appear). Obviously y'all can't tell me any better than my shop guys can if my fork is damaged, but would that be a potential culprit, or is it more likely a poorly selected top tube lettig the whole frame flop around?