Use CIWS for all the PD. That solves the missile problem while leaving it open to fighters.
However, I do want the Death Star to fall to missiles, just not those fired by capital ships.
The fix, as I see it, twofold: 1) Make missiles extremely short-ranged, but fast and powerful. 2) Only give missiles to fighters and gunboats (to replicate the Millenium Falcon, et al).
Sure, aliens will tear up my death star and capital ships, but standard Star Wars vessels seem to do poorly against such foes anyways. As long as my fleet is internally consistent, I've got no problems.
I might develop CIWS and missile-tracking fire controls that won't work against the "Star Wars" weapons, due to the speed of the missiles. I'm also making the compromise of photon torpedoes being missiles, as otherwise I need to have invaders on and take them out prior to setting up my fleet.
I'm also going to rename the ground units to match Star Wars. Here is my Conversion Chart:
Mobile Infantry -> Imperial Army w/AT-STs
Assault Infantry -> Imperial Army w/Speeders
Heavy Assault Battalion -> Imperial Army w/AT-AT support
Marine Company -> Stormtrooper Company
Marine Battalion -> Stormtrooper Battalion
Garrison Battalion -> Imperial Army
My rational is spoilered and based mostly on the West End Roleplaying game, and some experience with Star Wars Battlefronts I & II.
Rational behind Imperial Army designation: They can't capture land without equipment, thus their role as Garrison and equipment designations for all higher infantry. Their designation as Assault Infantry when armed with speeders is due to the increased mobility that the speeders provide, which is a great asset on offense but makes them less able to actually hold ground.
Calling the mobile infantry Army with AT-ST support harkens back to their mostly defensive role with such armament in the movies (defending Endor) and the relatively slow speed (compared to speeders) and weak armor (compared to AT-ATs) of the AT-STs.
Another way of thinking of it is like this: If the AT-ST-supported unit lost it's AT-STs, it would be identical to the standard Army unit, because most of the troops aren't in the AT-ST (they're dedicated military hardware which only hold two people). If the speeder-supported unit lost its speeders, half the troops would be dead, as they were riding into battle in the speeders (as speeders are civilian craft converted to a military role, and are thus more common and hold more soldiers).
I'm open to ideas, if anyone has them.