Here is my (educated?) guess... I had the same problem after I installed my new 347, new FRP aluminum drive shaft, and new Centeforce clutch. This vibration that started at about 3000RPM. Drove me nuts. The engine parts were supposed to have been ballanced. However.... I took the engine back out and took all of the rotating parts to a different ballancing shop and spent the $200 bucks to have it done again. Wha La... no more vibrations. All this to say that I suspect that you have something out of ballance up front. Harmonic ballancers can cause this problem especially the ones that have a rubber isolation spacer. The outer ring slips, rotates out of positon, and causes the imballance. I would first of all replace the harmonic ballancer. You are not going to feel the vibration if is tires or any other moving part if you are sitting still in neutral. Hope this helps.
89LX fastback, 347 Probe stroker kit, P.C. rings, Clevite 77 bearings, Crane hydraulic roller rocker cam, Edelbrock RPM Performer intake, Holley 670 Street Avenger, Victor Jr. heads, BBK long tube headers, Performance Automatic Pro Comp C-4, MSD billet distributor, Blaster 2 coil and 6AL box, B&M Mega Shifter, 410 gears with 31 spline axels. "Get in, Sit down, Shut up, and hang on"