Option One:
1B Mike Carp
2B Jose Lopez/Chris Woodward
SS Yuniesky Betancourt/Ronny Cedeno
3B Russell Branyan

Option Two:
1B Russell Branyan
2B Chris Woodward/Ronny Cedeno
SS Yuniesky Betancourt
3B Jose Lopez/Mike Morse

Option one is the more unconventional answer and certainly punts defense a bit, but let us have a look at the numbers.

DEFENSE

Option One: ?/-5/-10/-10. Total: -25
Option Two: -5/0/-10/-5. Total: -20

Based on UZR, with some question marks as to how Mike Carp and/or Jose Lopez would field given sample sizes, but some legitimately horrendous prospects of seeing Mike Morse on the field. All in all, it looks like it could be about a five run difference or so. And I feel like I am being conservative toward the more traditional option two here. Worth noting is that by moving Branyan over and inserting Carp at the corners, you leave Woodward and Cedeno both open to sub in at the middle infield positions. In the currently proposed Option Two, you are losing half of that flexibility.

The key here is how bad you think Branyan would be at third base. Branyan's actually been mostly a third baseman lately, logging almost 2.5x as many innings there than at first and logging significant time there as recently as last season. His career UZR/150 at 3B is -6.9. I've projected that all the way down to -10 to further worsen the case against.

OFFENSE

Mike Carp's projected wOBA: .323
Chris Woodward's projected wOBA: .287
Difference between two, over a full season: 20 runs

This operates under the assumption that the normal starter's offense does not suffer from moving positions. All numbers come from updated ZiPS projections.

Do it, Wak. I know you love defense. We love it too. But what's more important than defense is offense plus defense and there's just no way to justify starting three terrible middle infielders while you let Mike Carp and Jeff Clement go to waste somewhere.