I usually add 1-2lbs of thawed frozen fruit to primary, inside of nylon bag. Then, when backsweetening, I use 2-3 cans of 100% frozen juice concentrate, in addition to sugar, to achieve desired results. The trick will be finding a frozen blackberry 100% juice concentrate. A good one I've used is Old Orchard Berry Blend, very berrylicious.
Some recipes call for muuuuuch more fruit in primary, but that $$$$$ adds up real quick, and my nylon bag only holds so much, and loose fruit in primary will cause more floating bits which will cause it to clarify slower.
Congrats on the upcoming wedding, and great idea to incorporate homebrew. I gave my groomsmen homebrew mead sampler packs when i got married last year and told them they got better with age. One of them drank 4 12oz bottles that night.
Have done this strategy to make SP with mixed berries, pineapple, watermelon and grapefruit, with good results every time, but its very hard to predict how long it will take to clear. Some were fast, others slooow.
Since time is an issue, perhaps nixing the fruit and just adding the juice concentrate at end would be faster?
Tried that with a Cherry Lime SP with good results.
Also, if you can (with SWMBO's approval) clear enough fridgespace to cold crash the entire carboy, that could speed up clarification that much more
Either way, 3 weeks is a stretch. It will ferment dry