The FAS is a hull tank, it will always be a hybrid build and the only viable shield for it is a bi weave. Some fly without shields at all which removes the need to manage pips but put you in higher risk of being module sniped.
The shields in the FAS are only used as an additional layer of protection, they are expected to drop and it is completely non issue, I have a G5 thermal mode with fast recharge as a special effect.
The FAS is naturally a jousty ship, and specially with frags there is no other way to fight. His mistake was keeping close distance and letting me outfly him with every joust. He had 4 rails and should have kept at around 3 - 4 kms from me as much as possible.
I dont fly the big 3 in PvP so I honestly dont know how to fight with them. I believe face tanking is a viable option with those kind of ships. What I can tell you for sure is that medium ships will always win by manuevrabilty instead of face tanking.