Hehe, way ahead of you. My core planets are now all within 5 overlapping PDs. Let's see you fighting your way through that. :-)
Do multiple PDs help? Will you get 3 chances at shooting down a fleet? If so, that's of some use.
But putting a PD on a big planet is a huge waste. PD should be placed on a low-pop planet with few expenditures and mind control at 65-75ish so that food never runs out. Then your big planets produce absolutely insane amounts of quatloos.