Something similar going on with the 2000 Ram I got for my stepson. The kid I bought it from got it stuck between 2 and 4. He pulled on the 4wd shift lever until it broke off and he couldn’t fix it. I bought the truck with 79k miles for $2500. Crawled under it with a hammer and the old linkage and banged it through its gears, back into 2wd. I experience the same exact shake as OP and your post makes me think that’s what the trouble is. Once I got mine back to 2wd and replaced the linkage, it still won’t shift through the 4wd gears. My plan is to just replace the transfer case, as the kid snapped the selector bolt off that the linkage attaches to and the only way to replace it it is to pull the case and split it open. For what it’s worth, I replaced the commonly failing snap ring with a “case saver” and still have thus issue. Still with checking because they do fail easily though.
