Most blackberry jam recipes call for slightly under-ripe and not-too-sweet blackberries.
If ripe and sweet blackberries are all that's available, is there any way to compensate with other ingredients or timing variations? More/less pectin? Cooking for more (or less) time? Varying the amount of sugar?
I make a fair bit of blackberry jam, or mixed fruit jam heavy on the blackberries - we have some growing at home (better for flavour than texture) and pick the others from hedgerows. This year they're particularly sweet and juicy round here as well as quite early (and this year we plan to make sorbet instead of jam from them), but this means we make it from a range of blackberries.
Taking your ideas out of order, so I can finish on the most important point:
Jam needs enough sugar to work properly, to set and keep. So don't reduce the sugar, but accept that the jam will turn out a little sweeter.
Blackberries have enough pectin anyway, at least for a fairly soft jam, but pectin works better in the presence of a little acid. A little lemon juice or a really sharp apple can improve both the set and the flavour of blackberry jam. If you can find smaller sharper ones growing wild, chuck them in. If you want it really firm, you can still add pectin
How you cook it is crucial. Forget any recipes that tell you to cook jam for a certain length of time if you want a reliable set. It's all about the final temperature. Wetter fruit will take more cooking (longer on the same heat) to reach that temperature. And this is one time I boil without a lid, because you're boiling off water until the boiling point rises to the desired temperature of 105°C (220°F). A jam thermometer is ideal (ensure it sits at the right depth), but the "saucer test" (BBC Good Food recipe) rapidly cools the jam on a chilled plate to allow you to test the texture.
