Uh, they're both 9 STM, and D moves aren't bad in this situation. The RUD is very fast if you learn the fingertricks, can be much faster than the alg you posted. There's also the fact that the alg I have is literally just an optimized version of your alg:
R' F2 R' U' R F2 R' U R2
Let R' = Lw' x', then we have Lw' U2 Lw' D' Lw U2 Lw' D Lw2
Note that Lw and L are interchangeable with regard to corner pieces, thus we have L' U2 L' D' L U2 L' D L2
Reflect across M and change beginning AUF to make the alg use more ergomonic R moves, leaving us with: y' R' U2 R' D' R U2 R' D R2