LVL Deflection

Hello, I am designing and building a covered porch in central Massachusetts. As a disclaimer I have no prior building experience. Because the second floor of the house is cantilevered, the porch is designed to be freestanding. I would like to tie the roof into the side of the house and flash it (not to hold weight but to create a gapless transition.) My questions are related to the beams labeled A, B, and C. Two different lumber yards sent this design to their engineering department and one came back recommending 9.5" LVL in 3 ply for beam A and 2 ply for beams B and C. The other recommended the same ply's but in 11.875". Is one over or under designed (they both used the same live and dead loads)? My second question is, both reports have some amount of deflection in the LVL, how can you install flashing when the beam/roof might sag up to a half inch under heavy snow conditions?