Interesting probem, Kate. It might help to trace the coolant leak. No drips from hoses, heater bypass valve, beneath water pump? Might be head gasket. I confirmed my HG failure by topping up header tank, running engine at idle until low coolant light came on; took an hour. No puddles under car, no sign of leaks, so I concluded HG failure.
Don't see how fuel filter would do it. Dying fuel pump might. Could be the mesh filter on pump intake partially clogged. No smell of fuel, is there? I have had corrosion around fuel pump outlet pipe create leaks.
In the olden days I have known faults like yours caused by icing in the air intake on misty days. Pipe get narrower, flow is restricted, engine finally stops. Driver gets out, scratches head, has cigarette, meanwhile engine heat melts ice. Driver starts engine, all is well again.
Other old problem was blocked fuel tank air intake. No air gets in, as fuel is pumped out pressure in tank lowers, eventually reducing fuel flow so engine loses power. Driver removes filler cap, relieving vacuum, engine then runs fine again. Easily checked, run it without filler cap.
Don't live on a farm, do you? Mice nesting in the air filter could do it.