I have always run cables at the front with no problem.
Every pro installation I have seen shows cables at the front.
...and I have seen plenty pro bikes run cables through the back as well. Either way works but what is correct and optimal is more a function of type of bars being used. If the bend from tops to ramps is tight (e.g. Easton EC90 SLX3) then you will want to avoid running der cables in front because the bend is nearly a right angle bend and much too tight (yielding increased cable friction). If the bend from tops to ramps is a gradual bend (e.g. Deda shallow or deep drop) then running cables on inside will work fine. However when cable friction becomes an issue then cables should be run through back, regardless of bar geometry . Specifically, when mounting cables on back of bars the der cable will follow a straight line when it exists the lever and threads through the ergolever cable guide, as opposed to being forced to make a tight bend needed for the front mounted cables. This is a critical point of friction and if poor shifting linked to cable friction is an issue then this is the most important point where you can avoid friction.
Campy promo videos for the shifters show cables at the front.
Campy now supply shifters with DR cables pre-installed and in the front position!
Just because they are pre-threaded in that position that doesn't mean that is the optimal installation (see above). I suspect they might pre-thread the cable to simplify packing (it is easier to bind and pack two cables together when they exit the lever as opposed to being separated by about 2 cm)?
To OP, looks like you might not have addressed the chain length issue yet? Also, what hanger are you using? In my experience stock hangers from some manufacturers are cheap stamped alum rather then machined ...this makes a huge differences in shifting. I exchange all my hangers with Wheels Manufacturing hangers which are both machined and consistently beefier (literally more material) then stock hangers. As has already been noted, proper length of rear der cable loop can also make a difference. Lastly, I would avoid the Gore cables all together...they might be slick upon installation but after just a bit of use the cable coating begins to wear and gunk up inside the housing. I have had better luck using Shimano der housing with Campy cables (the only Shimano product that touches my bike)...the Shimano housing has a slightly larger liner diameter and yields less friction all together (this was per recommendation from DaveS...who interestingly has yet to weigh in on this thread?). See pic below illustrating rear der cable loop and chain length...EM3