I don't know Alec. I was just looking at the originally posted cartoon? Liked your drawing very much as I do all your drawings. Just questioning the presence of limit switches based on the original cartoon and the use of a momentary DPDT switch. I wish we all knew the big picture on this. Like what is supposed to happen and why?
I noted that the terminals shown are for the standard Bosch Automotive relays. This website sells two SPDT relays for reversing: **broken link removed** They can usually be found cheaper.
You have a 3V signal and that can't activate the relay(s) on it's own. It needs help from a transistor and suitable base resistor.