Bad Vibration Under Acceleration At Any Speed

Beautiful car. I am baffled why the driveshaft came apart before the 7.5" rear end. You mention 31-spline axels, and using a carrier from a 7.625 F-body - did you mean 28-spline? You have me looking sideways at the shortened stock driveshaft (new u-joints) in my 5.3L/4L60e Monte Carlo.

When you find what is vibrating, it will be obvious.

Yrs ago I replaced a ring and pinion in a s10 that lost a driveshaft. Bent the pinion.

I hope my previous entry wasn't too long-winded, plus I noticed some typos in there that I need to fix.

My main point is that after listening to your description, I looked at everything from front to back including the possibility that even the cooling fan might be bumping into something under acceleration. From looking at your photos it looks like you have electric fans and if that's the case then that immediately rules that out.

Two main areas that I see is torque converter and the sprag that's in the Turbo Hydramatic 350 which is a well-known weak point of that transmission. However if those were the issues or contributing issues you would be having the vibration even under "coast".

Friction of rest is greater than friction of motion, that's just the basic physics. You have reciprocal action changing to rotational action and then the actual rotation of the driveline which is basically the full system starting at the crankshaft and going all the way back to the pinion then the 90° redirection and to the axles and the axle bearings.

This is one of the reasons I said to check your mounts. Starting at your engine mounts your transmission mount and even the secure tightness of the Cross member. Any of those items being loose under acceleration the engine will rise and will shift the axial rotation and that in itself can cause vibration. If all of that is good then you can rule that out.

You can already pretty much rule out transmission trouble, and previous mentioned drive shaft issue, so it seems to be pretty obvious that the vibration is coming into play under acceleration that is somehow related to the replacement of the drive shaft and possible damage to the rear axle.

So at this point it ends up being a little bit of a cost benefit analysis, due to the fact that you're going to replace it with the 9 inch unit. You might end up finding that after you do that, the vibration goes away. If it does, then problem solved.

If it doesn't, you still have the other issues to look at that you have already mentioned. With all that said, I feel that the issue is somewhere from the back of the transmission and into the rear axle somewhere.

You say the rear wheel sustained some damage, have you checked for damage on the rear control arms, both upper and lower? A slight bend could be causing a bind while going through its range of motion.
Just another item to check off the list.
I made the mistake of boxing my upper and lower control arms and adding polyurethane bushings with Lakewood No hop bars on my 79 406 Monte Carlo. Car developed a vibration on acceleration almost immediately which I attributed to the no hop bars. This past summer when I parted this car out I found the rear was in such a bind with the poly bushings and boxed upper control arms that it wallowed out the upper mount on the no hop bars. I understand this is an apples to oranges comparison but a bent control arm could be your culprit.

Could you get therear axle up with tires off the ground supported of both sides with jack stands of wood blocks high enough to get under car physically?...maybe have someone inside..to put car in gear ( I have used a board James from seat to gas pedal) to hold gas at say 1800 rpm .Okay while you are ironed dangerously close in front of rotating tire close enough to se what the rotating driveshaft is doing !...check front and back to see if you got as much as 1/16"(max) runout at either end ( or center).determine said runout to be in pinion yoke or at the front input ....if your satisfied both ends are not wobbling ect..Shut car off and while you got your axle up take a can ( like pork and beans ect) AND SET iT CLOSE TO YOUR TIRE"... as close as you can get it with out it being moved out of place ( very close by tread) said can ( of beans ect)in place" rotate the tire by hand ( trans in neutral) with the can sitting close and watch tire were it touches and dosnt ( Dose tire have a higher side? )here the figure is 1/8" and plus .Assuming you took a drive prior to doing this test , ?to warm tires up first.?..you can interpit the figure 1/8 " as the ( limit)amount of runout in tire you can tolerate with out ( seriouse)vibration . Say if you have 3/16" runout in the can test ( tire symmetry) get a tire or a pair , it's possible for new tires to flunk this test okay ?..Remember what ever happens on the rear tire gets transmitted to the front through control arms then frame ect sort if setting up a counter vibration( sea saw)..you may find your differential yoke is not centering the shaft .might just need a different yoke youl proubly need to tighten it twice if you change it to be certain crush collar is sqeezed enough .if you ever hear a zizing sound as your car is slowing (10 mph)down on the factory gbody's" rear ends, the pinion preloaded is to loose and the pinion is possibly touching the ring ( correct me if im wrong) this ( zizing) has to be fixed asap...Aside from that you stated it had a different setup then factory so just saying..consider nexus or Goodyear possibly bf Goodrich ect..other likely explanations are posted above thanks

Following, I have been fighting a vibration for the past year.