"I've found that any feature branch that lives longer than a week becomes essentially impossible to integrate - in the time necessary to bring it up to head, head has changed enough that you then need to integrate it again, and so on."

DCVSs don't stop you from doing your commit, doing a naive merge, and then optimistically pushing. That option is still there, and is partly why so many people rebase before pushing their changes. Of course, pessimistic integration is equally available as an option.

If you find the overhead so high, it suggests that it's process holding you back and forcing you to pessimistically integrate, rather than the DCVS doing so.