I think the test runs will get progressively better up until September, just because raspberries don't really come into season until Summer.
I'm doing a fruit hef this weekend - thinking about trying some un-preserved jam to go along with frozen blackberries (maybe some pineapple?). I'm adding in secondary (and will try the lemon zest, too!).
Learned my lesson a long time ago - PUREE if you're using a carboy. Strain if you're using a fruit with lots of seeds (raspberries, blackberries, watermelon, etc).
Be sure to account for the volume and sugar contributed by the fruit. Even a small amount of raspberries can increase your ABV enough to thin out the beer and leave it unbalanced and unpleasant.