Instead of running another lower lifeline, why not add 1/4" nylon line crisscross fashion between the stanchions from each stanchion to the toerail. Use a continuous piece of line running from stanchion to toerail and back up to stanchion etc. This would give more probability of catching you if you were to slip. OTOH, a good SHORT tether is better. If you are on the port side, attach to the starboard jackline and vice versa. You might also want to simply use lifeline netting and a tether system.
My 28' S2 has only single lifelines and I considered adding lower ones but decided other netting and tether was actually safer.