Will the constant strain on the shrouds cause a problem???
Constant load on the shrouds is a is actually the least you should be worry about. Your shrouds are rated for static loads in order of 1000 lbs. The issue is a fatigue from wind tossing your mast back an and forth. All your standing rigging, including all the hardware connected to it, will by under dynamic and repetitive loads resulting with premature wear. This is not much different from storing your H16 with mast up year around. For this reason, the best is to store your mast in down position.
As others said, a lots of tie downs is a good idea. If you must keep your H16 with a mast up, I would put a lots of bungees to restrict mast from tossing around as much as possible.
BTW, I envy your location! Here in central BC, sailing season is over and otherwise winds are light. I happen to visit Sechelt last summer and I was drooling at the water properties like yours.