Okay, I think I came up with a decent idea:
Should be self-explanatory. Same process happens in reverse coming from the other direction, it's a symmetrical design - pretend that netherrack block at the top (under "k!*") has a button and a powered rail there. Could also have a detector rail where the "2" arrow is instead of a button and use that to set a delay timer to automatically kick off your cart again if you don't get rid of it in 4 seconds or something.
This has kept me up late enough for tonight, will maybe try to implement tomorrow