I don't wanna go back to that famous argument about which determines the ball reaction most, but in my experience, surface is the primary factor.
I'm not saying that it doesn't matter which type of cores you choose. It is for sure that in some cases, some core-surface combination may suit your style, release etc. better. Of course with a certain drilling which suits best with those particular conditions you are bowling as well as your style.
However, I believe that solution of getting down the lane more easier is not directly related with symmetrical-assymmetrical core selection. Weaker/high RG drillings together with a smoother and/or polished surface will help better.
Regarding drilling:
Pin placement above bridge or even above the middle finger will give you more length to clear the heads easily (pin to PAP distance 5" or more).
Only exception in that advice telling you to use symmetrical cores, that person might meant 3 piece weaker cores.
What I kindly advice you is to find a good ball driller who will watch your game first and consult it with him/her.
Hope this helps..
Burak