See attached schematic.
The end result is a latching relay schematic. When start is pressed it latches, when stop is pressed it unlatches.
I’m pretty sure this will work as intended but I figured I’d get a second opinion.
When you press start, it will activate the n-ch mosfet which in turn activates the coil which triggers the contacts and its a standard latch.
When you press stop, you turn the mosfet off, the 100K in series with the coil will de-activate the coil which cuts the 5V source from the circuit.
It would be simpler is I just used a NC push button to break the latching but it turns out that there are not many NC tactile buttons that are cheap, share the same footprint/look as its NO counterpart and are PCB mountable. With this design I can use the same button type for both start and stop.