Fat aluminum and fat conduit are your friends here.
We'll start with the conduit -- Schedule 80 PVC won't go anywhere when you put it in the ground, is plenty rugged enough to survive what a homeowner can toss at it when brought aboveground, and is available at the orange borg, in sizes up to 3". Since the electrician won't be there to bail you out with the truck o' pulling tools anytime soon, go with the 3" size even though we're only at about 10% fill here. Bury the conduit to 24" -- that will guarantee your 18" of topcover. As to the terminations -- it will come up the outside of the buildings in question into LBs that then go into the building sides.
Then, we pull out the jumbo aluminum wire. For the price of your proposed 6AWG THHN/THWN-2 copper, you can get 1/0-AWG(!!!) RHH/RHW-2 AA-8000 series aluminum, and since this is a feeder, it's going from aluminum breaker/panel lug to aluminum breaker/panel lug anyhow -- if your insurance complains, tell them to go re-read NEC 310.106(B). That aluminum, by the way, will carry 120(!)A -- 100A is a more practical size, though, so we'll use that instead. With that, you can use an 8AWG bare copper ground wire.
Sorting out your subpanel
You'll need a NL20 lug to land the ground wire on (instead of that kludge-screw) and a BR2100 breaker with a BREQS125 hold-down kit to serve as a submain. The orange borg can order all these in if they aren't already in stock there. You'll also need a torque screwdriver for this.
The hot wires, then, will land on the terminals of the BR2100, which is your service disconnect (you can backfeed any breaker that does not have LINE/LOAD markings on it). The neutral lands on one of the big neutral bar lugs, and the existing kludge-screw is replaced with the NL20, which is where the ground wire is landed. Make sure to torque all connections to spec and use anti-oxidant on all aluminum wire terminations so they don't come loose and become a sparky mess later!
Landing the feeder in the main panel
If you want to bring the new feeder up to its full 100A capacity, you can put another BR2100 breaker and NL20 neutral lug in the main panel in place of the BR240 that is currently protecting your feeder, terminating the ground on the existing bars. Of course, if you have a big lug spare on your main's existing neutral bars, feel free to use it, and you can run the 1/0 at 40A by pigtailing it with Al7Cu or Al9Cu lugs to smaller wire if you wish to postpone the main panel rework until later. Again, remember to torque all terminals to spec and use anti-oxidant with the aluminum wire!
Getting grounded
You'll need a ground electrode at the shop since it's a detached structure. Contact your local electrical inspectors (aka Authority Having Jurisdiction or AHJ for short) and they'll be able to guide you on what to do given your atrocious-sounding soil conditions. (For instance, a concrete-encased or "Ufer" ground would work if you had reinforcements handy to ground to, but not every pour has such.) Simply shoving copper rods 8' into the ground may be a waste of copper, though, in that it may not yield acceptable results in your situation.
No matter what you put in for a ground electrode, it can be connected via more of that 8AWG copper to the shop subpanel provided you protect it from mechanical damage. The neutral and ground being kept separate at the subpanel, though, is absolutely correct despite your seeming bewilderment at this discovery -- neutral is grounded at the service entrance and nowhere else.
Best Answer
Close, but not quite a banana
You are close to a correct setup here, but there is an issue: your specified conduit burial depth is too shallow for PVC under normal conditions. Code requires the top of the conduit to be 18" underground for a run through a residential yard, so you'll be trenching to about 20" deep.
Also, I would upsize to a 1" or 1.5" conduit here to ease pulling, and make it Schedule 80 instead of 40 as the former is more rugged against mechanical damage than the latter. You will also need a pair of prefabricated wide-sweep elbows to bring the run aboveground and expansion fittings aboveground at the transitions to compensate for earth movement.
As to the wires -- 8AWG THWN is a suitable wire size (a bit more than strictly necessary here, but fine nonetheless), and you'll need to run four wires in the conduit: two hots, a neutral, and a grounding conductor -- the ground here is critically important as it serves a very different, and complementary function, to the ground rod at the outbuilding. (Namely, the ground wire returns wayward utility power back the way it came, while the ground rod is for returning wayward naturally (aka lightning)-induced surges back to terra firma.)
As to why 240V? This lets you balance the loads across the two legs of the feeder, reducing voltage drop, as well as providing 240V for the next bloke who owns the place.
The part about laying the entire conduit run and then pulling the wire through it is essential to avoid damaging wire insulation and jacketing excessively. You can use a shopvac to suck a foam "mouse" (or even a plastic grocery bag in a pinch) tied onto a length of twine through the conduit to serve as a pulling string, and then tie the string off to the wire and use it to pull it back through, though.