The repeater, 2-step:
First pic is with everything unhidden, second is with everything but the track itself hidden. The ramp direction isn't shown in this one, but I believe it's NW for both. The southernmost plate, p0, is linked to the lower bridge, b1 (this plate is used once only, though it is
not a one-use plate). The middle plate, p1, is linked to the upper bridge, b2 (the bridge of the next cell in line). The northernmost plate, p3, is linked to the lower bridge (the bridge of the next cell in line).
The southernmost pressure plate (p0) primes the system, retracting the bridge in the first 2x2 cell (b1). I've had some issues with this 'taking', so you may need to push the minecart into a harmless wall a couple of times and replace it until the retraction happens. Once you push the minecart in, it'll move within and between cells indefinitely and not touch this plate again.
The bridge in the first cell (b1) is retracted due to the priming plate the minecart has been placed on (p0), and so the minecart takes the corner beneath. It rolls continually over the pressure plate (p1), blocking the exit from the
next cell (retracting b2), and continues to do this until the priming plate (p0) deactivates and replaces the bridge (b1). The minecart now goes straight across the bridge and into the second cell, where it is held there by the action of the previous cell's pressure plate (p1) and continually rolls over the second cell's pressure plate (p2). About 200 ticks after the minecart leaves the first cell, the bridge in the second cell (b2) retracts, allowing the minecart back into the first cell. It is held there by the action of the previous cell's pressure plate (p2), and continually rolls over the first cell's pressure plate (p1)... And so on.
You may be able to do without the priming plate depending on the placement of the ramps and other plates. Pushing a minecart straight into a route that avoids any pressure plates but the one in the first cell will do the priming plate's job, because the minecart will be entering the first cell while its plate is activated and no other one is, in theory at least.
The latch, or the potential for one -- this is just a lever-operated pressure plate, and the more I think about it the less useful it becomes:
This one's simpler. You have a small loop with no pressure plate, and overlapping it is a larger loop with a pressure plate, and you just push the minecart in. If the bridge is retracted, the minecart turns the corner and remains in the small loop away from the plate. If the bridge is out, the minecart jumps to the section of track with the pressure plate, taking the larger loop and keeping the plate active.