I have no knowledge of the R770 specifically but I am familiar with the 440, which is a step down in the series. The R440 (or 4403) fd has a mountain bike cable pull, and a road bike curvature. So a 440 front shifter has a mountain cable pull, and I would assume the 770 does as well, meaning it would not be happy with an Ultegra 6700 FD, or a 105 FD (old or new).

All the statements I had ever seen about the 440, 550, and 770 said they had to be used with a like numbered FD. I actually use a SRAM X7 with my 440 FD and it works beautifully.