Honestly I think the drive looks pretty good. Transverse e.j.'s would have prevented any side to side movement, imho.
This is going to be long again. Fixing these types of things is difficult to put into words, but fairly easy once the basic concepts are understood.
The piers will likely do little to resist over time. The forces moving the slab sideways will almost certainly push the pier over, or plow it through the soil. If a long deep curb had been put in place of the piers, ir would likely still move. It almost certainly is the expansion contraction.
I sketched up a little drawing in iso view. Think of the cleat as a transverse curb, or anchor pushing back against the slab forced as the concrete expands in the summer heat.
Your pics include on of the pier where a sealed crack in the drive slab adjacent. That is a good indication the slab is moving toward the pier. and the crack appears as that edge stretches outward.
In the upper left is a representation of the rebar layout.
If mine I'd put transverse bars at 6" apart stacked vertically and about 8' apart vertically.
In the lower right is a cross section of a slab with correctly placed sealant. The top is the sealant in a hot day in the summer, the bottom on a cold day in the winter.
Ideally the sealant hould be placed in the mid temperature range.
It appears the joint was routed before the sealant was placed? Just a guess. It's very good to rout (with a special router) any cracks to be sealed. 1, it removes old sealant, 2, it cleans dirt and other material from the surfaces, and it eats and drys the concrete. Alternative methods can work carefully scraping to the depth to be sealed, and using a wire brush on a gas powered lawn edger, etc.
If the wrong sealant is used it won't properly stretch and compress and can shear off the concrete (appears yours did this) and if too stable it won't compress at all and may continue "pushing" the slab outward as the temp cycles. It would the ultimate if you could find a contractor that can do "rubberized hot pour" These guys know how to properly prep and place and are in and out. Gheck with the local road maintenance dept, or airport, When they have a contract going the workers love pick up work for beer money. You may want to look up cold pour also.
If it were my driveway I'd first remove the de-laminating sealant and re seal with a quality product made for the purpose (of expansion and contraction). I'd then create a few new transverse expansion joints where you are seeing the most movement. Say, 3 cuts spaced 25' apart. A wheeled concrete "wet saw" can be used to cut across the slab and put e.j. sealant in there. depending on the width of cut (I'd shoot for 1/2") it will take a couple accurately cut passes, or, have a contractor rout any single blade width cuts. Contractor rental yards will have these various tools ar pretty reasonable rate, and contractors should have them already. The transverse cleats could be placed where the e'j locations are if it's found they are required later.
Keeping the cracks sealed as you are is a great plan. Water intrusion will wash out the fines of the base sand/gravel and freeze thaw will accelerate concrete deterioation. Keep water draining away from the sides of the drive by grading to slope away.
Don't fret about all this info as I really don't think the solution is going to be big budget.

The pictures help a lot.

Was the original driveway a steady grade when the concrete was poured,
and has the “dip” slowly appeared over time? the dip has always been there

Just after the original concrete pour,
was the center high
and edges low?
( was there a “crown” ) A light crown so the water would got to the edges

I assume there is no wire mush in the concrete? CORRECT, bad allowance on my part, as he asked if i wanted wire fence, reboar or fiberglass reinforced. I left the choice up to him as I figured he SHOULD know best

The T junction picture brings up the issue of
periodic winter rainfall causing water inundation of that lower sect,
particularly the far side of the lower section opposite the T. The area atthe junction and below ahs bee pretty stable The section that extends to the building does have some drainage issues that do need to be addressed mainly near the front of the building.

Freeze/Thaw caused
contraction/expansion
would seem the root cause
made worse by saturated subsoil
that freezes unevenly
creating left or right transverse forces.

Cut more expansion joints,
clean out existing joints,
re-cauk.

The uphill side of the T-junction needs a drain that passes under (or through) the pavement of the side driveway. that area is actually sloped up and towards the front of the bldg. See the preceding comment

A really tricky contractor
would lay a rubber bladder filled with water along side a shifted concrete section
anchor the bladder rigidly with stakes on one side
and let an overnight winter freeze
push the concrete slab back to its original alignment.

The pressures ice can create are one of Nature’s true wonders.

I believe I am getting a grasp of your recommendations which is to cut more 1/2" joints across the drive where the movement is most noticeable and reseal. This I'm guessing will reduce both the expansion & contraction as the slabs are now smaller, Correct?
The two I don't grasp is "The transverse cleats could be placed where the e'j locations are

The least amount of concrete would have been poured if the driveway slabs were flat bottomed and a consistent thickness.
We must assume this as “the worse case” since the contractor would make a higher profit.

But a knowledgeable professional would have made both lengthwise and transverse “ditches” in the subsoil before the concrete was poured to create concrete “cleats” meant to help the slab resist sideways and downhill drift. Since most cracks occur near edges it is good practice to make the concrete thicker at edges, and especially at corners. On automobile driveways it is good practice to make the concrete thicker underneath where the tires will roll.

Combine these two “practical tips” and the unseen bottom of the concrete will not be “pool table flat” but rather “lock and key” hugging the subsoil.

Ultrasonic thickness testers could be used to see if this varying concrete thickness exists. Ultrasonic testers are way cheaper today than they were in the 1980s.
A cheap IR Temperature gun could also be aimed at the driveway on either a very hot or cold day. On a hot day the thicker concrete might read a bit cooler than nearby thinner. After a cool night it might read warmer.

If Superman is flying overhead just put a Lois Lane look-a-like in a skimpy dress to wave him down for a quick X-Ray vision.

If the ground under that driveway is loess
then it is AMAZING that you have had so little trouble.

Let’s hydraulic hammer it all to pieces
take pictures
and publish an article in Engineering Monthly magazine
titled “Minimal Sift Pavement Design Survives a Decade”