Starters shouldn't be too strong; about 1.04, generally. Do you have a hydrometer? If not, I highly recommend getting one; they're cheap, and often considered an almost essential tool in beer and winemaking. Past that, it will be difficult to figure out how much sugar is in the strawberries, unless you use a commercial strawberry juice with nutrition facts.
I would also recommend adding lemon juice in increments to the starter. That will help prepare the yeast for the shock of a highly acidic environment. Hard lemonade can be tricky because of this; yeast doesn't much like all the acid. You want to get them as prepared as you can.
I like the idea of making a hard lemonade with some strawberry, though. Strawberries and lemons are the perfect complement, especially in summertime.