Procrastinating on the big test, i spun something off my toggle memory cell. While i couldn't come up with a decent way to make it smaller or more powerful, the core principle looked like just the thing for a powerless ring counter (could be used as a program counter or somesuch):
z+1 z+0
▼▼╗ ══###
#.║. #####
.#GH╗ ##▲▲#
..#.^ #####
G - Grate over down ramp (engraved with EW track)
H - Hatch over down ramp (engraved with EW track)
^ - pressure plate on flat NS or SE track
Of course, there are several more of those covered pits; the cart proceeds from Northwest to Southeast through the counter.
There's one hatch and one grate over each pit, all operated by the same pulsed signal. Between signals, the cart is in one of the pits, bouncing back and forth. When a signal arrives, the hatch opens, cart exits, takes the corner to the south and proceeds to the next station. There it'll stand on the grate, since grates have a 100 step delay, so they haven't opened yet. After ~100 steps, all grates open - and all hatches close. The cart falls off the grate into the pit below, but cannot leave because the hatch's closed already. Another 100 steps later, the grate closes and the counter is ready for the next signal. It's important to use grates (or floor bars) for this purpose and not bridges - bridges toss stuff around and can throw the cart off the pit instead of dumping it inside.
Output signals would be sent by pressure plates on the tiles southeast of the hatch. This ensures that the on and off signals are far enough apart to operate a bridge, floodgate, grate or bars (the tile just outside the pit is a checkpoint and the cart crosses it in a single turn, which _toggles_ 100-delay buildings instead of "cycling" them).
For added weirdness, retracting bridges can be built over the tiles just outside the pits. When retracted, the cart will simply round the corner. When extended, the bridge obscures the corner and the cart travels in a straight line, allowing cart extraction, aborting processing or implementing program "jumps". I built SE track corners instead of straight NS track directly north of the grates to enable alternative pathing.
Tested and proven.