Is this maybe an ignition related problem? Does it shake the whole time it is in lockup or just as it is engaging? If it does this the whole time it is in lockup then I would suspect the plugs, and wires should be looked at. Did you happen to find out when the last tune-up was done? If the plugs and wires are recently replaced I would then move on to the coil packs, ICM, and also the injectors. There is an article in Tech Info to check the coilpacks, and I would clean the contacts on the ICM while they are off. As far as the injectors go there are rare cases of bad or wrong injectors which I had. When I bought my 93 I had a bad bucking in lockup and it turned out to be that someone put in a completely wrong injector. I switched the injector with one from the yard and it ran like a dream.
Welcome to the club.
1993 Bonneville SC SSE With Supercharged Badges, Black and Gold, CAI, 180T, TR-55'*, 2.2 Pulley, Jet Stage 2 Chip, Ceramic coated PEM'*, Magnaflow, Flowmaster 80, Megs Tips.
1995 SLE (Wifes), White and Gold, CAI, APN, Magnaflow, otherwise stock.
1966 Ford Ranchero, 312ci 60 over block decked, GT40P heads Milled, RPM Air Gap intake, Holley 600, MSD Billet Dist., 6A Box, FlowTech Shorties, C-4 W/Shiftkit, 8" 4.11