Well, let me throw some new info into the discussion.
We have a "master gardener" program here in Oregon & I suppose the Extension Service runs similar programs in other states. A master gardener told me last week that herbicides actually work better in the fall. I do know that is true in regard to killing blackberries, Scotch broom and other hard to kill perrenniels with Roundup. Roundup really does a job on them in the fall, but as with most herbicides, the label says to use it when the plants are actively growing. The reasoning for using it in the fall is that the nutrients are being translocated down to the roots & they will take the herbicide with them. Does not make sense for annuals. Since clover is a perrenniel, I thought the master gardener might be right.
My herbicide of choice for my lawn is Weedmaster, which is a form of 2,4-D & dicamba. Labeled for bur clover, not white clover, but it is not labeled for blackberries & it works pretty well on them & Scotch broom, too--in the spring.
So we have contradictory info and recommendations. I think I'll give it a try in a couple weeks & I'll report back when I can see results. Don't expect an answer soon as you don't see results on blackberries for at least a couple months.