It seems like the entire vehicle just starts

It really sounds like your front tire is out of balance. Bring it to another
tire shop. Balancing a tire correctly isn't as simple as one would guess.

have them check the radius arm bushings, and sway bar bushings if the tire
rebalancing does not fix it.

You could easily be describing a bad u-joint in the driveshaft.  It can
act just like you describe and the sound/vibration is really sneaky
about 'seeming' to come from one area or another.

To check them, you need to block the wheels and put it in neutral so you
unload the drivetrain, if it's in gear or park it cannot be tested, then
go under and look for any slop or rust stains around the u-joint caps.
Only 'no' play is acceptable and if you see rust stains, that usually
means the needle bearings are dead or very soon about to be dead.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's

IIRC, you have a 2 piece drive shaft in that one.  If so,
check the center support and bearing very closely.
Sometimes the rubber deteriorates and lets it more or less
float free causing a vibration.

Lugnut

Hello Jay,

To start, have your tires checked for balance, spin balance not "bubble"
balance. At the same time have them checked for "out of round" and "true"
(side to side). Check for bubbles in the tread area (tread separation) and
broken steel belts (twisted tread), also watch for deformations in the
sidewalls (broken body cords). Some of these conditions are a blowout
waiting to happen. Also, check to see if your wheels are bent, cracked or
have broken welds or rivets.

Have your wheel bearings checked, make sure they are lubed and adjusted
properly. Rear wheel bearings are lubed by the gear oil in the rearend,
make sure it is full. On drum brakes, make sure that there no loose or
broken parts floating around side the drum. If there are, they will be
trying to lockup your wheels (this can sometimes feel like a vibration,
however this usually makes a grinding sound).

As noted in other posts, check your u-joints, center support bearing and
slip-joints. Make sure all are tight, with no powdered rust coming out of
them. Make sure there is no play in them, rotationally, side-to-side, up
and down or front-to-back. Replace and lube parts as needed.

Also, the driveshaft may be out of balance, or it may have been
reassembled wrong at some time in the past, this will most likely have
happened at the slip-joint at the center support, all u-joints "MUST"
line up. Or, you might have a bent drive shaft, not to likely, but I have
seen it.

Be sure to block your wheels, or support the vehicle on jack stands,
before placing transmission in neutral. (I like jack stands, gives me more
room to work.)

Any of the above problems can give you the problems you are describing.

Oh, two more I was forgetting about, a vibration dampner that has
"shifted" and a cracked flex plate. The only one of these problems that
stepping on the brakes will have no direct effect on is the dampner, as
there is no change in the loading on that part, only the engine speed.

If you get no vibration while sitting still, in neutral, while changing
engine speed, then it is probably not the dampner. A cracked flex plate
vibration will normally only show up while under load, unless it is very
severe.

Some of these problems will very hard to spot in the shop, unless one is
very through and willing to take the time. Some of these are easier to
spot during a road test, with a "chase car" to look for problems.

Yes, I have seen or experienced all of these problems. Once I had a tread
seperation on a right front tire, mimic a sever vibration in the left
front, before coming apart and beating the hell out of the right front
fender and ripping out the inner fender liner.

I once saw some retread tires that were so out of round, that the only
thing that allowed the owner to drive his truck in to the shop was the
trucks soft "worn out" suspension.

Yours,
BigDave

Another update:  As I said before I put in new U-joints with no improvement
and the driveshaft is the one piece type. I have pulled the driveshaft out
again and now that I look more closely I'm noticing further issues.  The
rubber transmission extension output seal where the driveshaft yoke meets
the transmission output has some small tears and is leaking slightly.  Also
there is a fairly large amount of play in all directions from the
transmission output shaft spindle.  ie If I put the vehicle in neutral I
can wobble it by hand.  Is this normal? I'm thinking perhaps I need to
replace the bearings in the output shaft of the transmission.  Would this
require complete transmission tear-down? Any thoughts as to whether this
could be the culprit of the vibrations?

thanks again
Jay