Assuming there's a need to keep the sleeve tight, you could use the same technique I use for "leathering" the eye of a wire splice.
Just heave the lacing tightly and having very slightly enlarged the last of the hole pairs, cross and tuck the ends so that the ends can make another half-turn, which leaves them emerging on the underside. For extra friction, you could take another turn with each end, though I have never found it necessary
Then simply Reef Knot the ends tightly , then push that knot beneath the edge of the sleeve, where it will not be subjected to damage.
Regards
Ceeg