Can't speak from center sheeting experience, but I have been working on tacking on gybing without facing the back beam.
On port tack for example, sheet in left hand, tiller in right. Helm gets pushed over, and as you move to center of the boat the sheet gets eased and you flop the tiller over, now holding the crossbar/tiller slightly past the blocks. Now as you complete your "roll tack" release your right hand and regrab the tiller. Move forward (facing forward). The left hand is sheeting in Main and the right has the tiller. Do a counter-clockwise pivot, placing your right hand/tiller behind your back. Now do the hand swap, final sheet/course trimming.
I can picture this working with the center sheeting, as I walk through it. Go ahead, get up from your computer and walk through the tack. Focus on keeping your eyes forward.

It is much the same gybing, the eyes can be forward. I tend to just set the tiller down on the far hull as I gybe so that I can grab the lazy spin sheet as I cross and hand over hand it in.

But this could all be cr*p. With the new handicap, lake racing against a monohull fleet, I have dropped 10 positions. I need to find approximately 5 minutes a race.