Something not stacking up here. If you swapped leads and the non-firing cylinder swapped with it, then that says there was a spark problem - with one pick-up or HT lead or plug cap. If it ran home on 1 cylinder, then fuel was getting through. Now you've changed the pick-ups and HT leads you say it won't work at all, that there are sparks - but no petrol. Strange to say the least if swapping the leads round/ replacing them has stopped the fuel getting through. Worth just checking fuel flow by disconnecting a fuel pipe and seeing how wet the floor gets. And checking over the float needle, filter above it etc, if the carb won't flood when you tickle it plenty.
But, as a first move, suggest you clean the slip ring on the mag with a bit of clean cloth (a bit of electrical contact cleaner spray wouldn't hurt too) through a pick-up hole, check the state of the brushes and springs on whichever pick-ups you choose before putting them back (plus HT leads and plug caps), then check the gap on the contact breaker for size and sameness on both cylinders. I'd do that before thinking of taking the head off. If it ran fine till you had a cuppa, and then ran on one cylinder all the way home, I don't think, from far away, that there is a fuel problem. Nor, on the face of it, a cylinder head problem. My bet is that you have an ignition problem. Could be that the magneto is starting to protest when hot - not uncommon if the windings or condenser are on the way out - but more likely something less serious and a lot cheaper. Am assuming the plugs are correct and not too knackered, as they seem to have worked OK, depending on which side had the good lead on it when it did agree to run!