Well, ... since you've got your 14 tramp laced tight enough to bow the side bars you know the answer.
"Tight tramps make fast boats."
If it were me, and it is about once a year, I'd use 3/16" or 1/8", right around there in metric, and lace the centre lacing and across the back and then tighten it up using gardening gloves and sometimes vice grips. Then another lace down the centre and tighten that up. Now the first lace is soft. How did that happen? So retighten the first lace.
Leave the whole deal to sit in the sun for a few days and repeat.
And since we're talking, I don't know what age your boat is, but you want the tiller connectors that come with the Hobie PN 1957 kit and not the tendon ones.
It's a great boat and huge fun for small investment in money and effort.
Stay safe!