Jay:

I'm certainly open to a plywood bulkhead. I was going to do one fore and aft. I often see references to "marine grade" plywood. What actually is the difference between normal birch plywood and the marine grade?

Most marine plywood is 'mahogany' in my area. Marine grade ply should be void-free and use boil-proof glue. Usually there are more laminations in marine plywood vs furniture grade or doorskins, IME. Birch plywood can be excellent quality (the 5x5 sheets from Europe) or terrible (the 4x8 sheets sold by my local HomeDepot). Birch is quite a bit heavier than mahogany plywood, so I don't use it in boats much.

Either way it's going to be encased in fiberglass and epoxy, right?

Yes. If you are using wood for the bulkhead, it's wood-core for the glass and epoxy.

I assume you shape the piece of plywood by your trial and error method, then remove it, glass the front and back surfaces, then install it with fiberglass tape and epoxy around the edges. Is that correct?

I think I used wood core bulkheads on a couple of kayaks years ago, and certainly for the 'air tanks' in the ends of canoes, but nowadays I use fiberglass for bulkheads. I laminate up 'a few' layers of glass/epoxy on a flat surface (mylar sheet, waxed glass, plywood covered in plastic - that sort of thing) and usually put something on top till it cures (another mylar sheet, pieces of wax paper, plastic, etc..) + plywood and weight. It seems a bit 'floppy' when it first cures, but it does stiffen up over time. also, once the bulkhead is bonded in place, it can't really flex. One nice thing about using glass is that you can make curved bulkheads pretty easily, if that's what you want (behind the seat).
I usually 'tack' the bulkhead in place with a few small dabs of 'Quikwood' epoxy putty - they are completely covered by the fillet later.
I bond the bulkheads in place with epoxy fillets thickened with silica - a fairly hefty fillet with perhaps a 3/4-1" radius does the job. On a few bulkheads I added milled glass fibers to the filleting blend for strength, but that seemed to cause problems getting a smooth fillet. The WEST filleting blend is excellent (and brown) but expensive. Use a ziplock 'cake decorating style' bag to lay the epoxy along the 'corner' and then use a shaped 'stick' (I cut something from an autobody squeegee) to form the fillet. Lots of good filleting tricks in the WEST Boatbuilding manual (download) BTW.

I'd use the same technique to install a glassed wood bulkhead.
Note I don't use glass tape, though it is stronger that way- you'd need to put on a fillet and then tape over top of that. Filleting from the awkward side of a bulkhead is enough trouble, without tape.

Here's another question: I had planned a fore hatch but not an aft one. I really don't think I need to store anything for the use I have intended for this kayak. Do I need to be able to get access to both sides of the bulkhead in order to install it, or can I tape it in place from only one side?

If you are bonding/filleting only from one side, you need to be careful to coat the wood edges with epoxy.

I would never leave a non-accessible space in a kayak. Good boatbuilding practice demands at least an inspection hatch into that space. If you are determined to avoid a hatch in the deck, you could put an inspection plate (pop-out or screw-out) into the bulkhead. I put an access plate into the fwd bulkhead on my OuterIsland because I couldn't reach the foot adjustment from the (small) cockpit - but I had a deck hatch fwd as well. I recall that Et has done something similar.

If you are putting in a fore hatch, I'd do the rear as well. If you are storing gear at all, it's better close to the center of the boat (i.e. behind the seat). If you are paddling in steady windy conditions you may want to move weight forward (paddling upwind) or aft (paddling downwind).

Another alternative would be to use air bags (full-zie, intended for sea kayaks, not the baby WW kayak type) in both ends and forego hatches and bulkheads altogether. When the Broze brothers built Mariners without cargo hatches, they installed a 4" 'armhole' screw-out plate forward, to help getting the bag (and gear) shoved into the bow (and retrieved from it).
I've paddled Mariners with air bags and it works OK, but if you are doing rescues and dumping water out of the boat, it's easier if you have a bulkhead behind the seat. Without a rear bulkhead, there's pumping required even with an assisted rescue. Keeping the cockpit volume small really helps when you get water in the boat. In my Frej, I kept the bulkheads near my back and feet, and I can paddle the boat confidently without pumping after a re-enter and roll. Without bulkheads (using bags in the ends) I'd have a lot more water sloshing around.

It is a LOT easier to work on hatch recesses, etc. before the deck is joined to the hull. I've done it both ways -retrofitting to boats, and building them into the deck on a new build- so you CAN always change your mind later, but it's more difficult.