New wires don't cost much, replace them with new copper core wires just to be sure it's getting to the plugs with all the strength possible. Only the better parts stores will have the copper core spark plug wires in my experience. Bring your old wires so they can cut the new to the exact length needed. As stated earlier you may not have 'enough' spark getting to the plugs to do the job. Does the impulse sound nice and strong when it trips? What model of mag?
Pull starting wouldn't have effected the timing. It sure sounds like a lack of enough spark from a tired old mag to me so far. Old wires will steal the snap away even when the plug fires just laying on top of the block. No good/bad test for them either is worth doing or believing.