My suggestion:

1. Create a branch
2. Merge daily from trunk to your branch and resolve conflicts.
3. Work until it's done. Your branch may be outside core development for several sprints.
4. Merge back to trunk.

There's no getting around the fact that it will probably get ugly. I don't envy you. In my experience, when you drastically change a project, it's easier to merge ongoing development into the new paradigm versus somehow merging the new paradigm into a now-changed trunk after everything is finished. Still, it's going to hurt.