I still don’t get how you can get more than c×t³ as a colonized volume.

With wormholes you could travel within that volume very quickly, which will certainly help you approach c-speed expansion faster, since engine innovations at home can be propagated to the border immediately. And, of course, your volume will be more “useful” because of the lower communication costs (time-wise, & presuming worm-holes are not very expensive otherwise). But I don’t see how you can expand the volume quicker than c, since the border expansion will still be limited by it.

(Disclaimer: I didn’t read everything there, mostly the section you pointed out.)