I'd suggest that you perhaps review this old thread:
http://www.travellerrpg.com/cgi-bin/Trav/CotI/Discuss/ultimatebb.cgi?ubb=get_topic&f=3&t=000460#000000
In it, Dr. Gizmo posts a Basic Starship Combat Cheat Sheet that helps a lot:
http://erik.jordan.name/Gaming/T20/BasicStarshipCombatCheatSheet.html
Here are some of my notations on the Starship Combat Cheat Sheet:
* Initiative is rolled only once, at the beginning of combat. (THB, pg 150, last paragraph, right column: "These initiative check results determine in what order vessels will act during each round of the encounter." Also, it's consistent with how initiative is handled in the D20 System.)
* Point Defense Sandcasters may be fired against incoming laser fire as well, according to the ruleset. (THB, pg 162, first sentence of Point Defense Sandcasters.) I agree with you that a sandcaster should not be able to react to an incoming laser moving at the speed of light, but I'm assuming that this rule represents sensors detecting the tell-tale signs of powering up immediately before firing, or something like that, as a justification for the rule being present.
* Anti-Missile is not required for laser point defense against incoming missiles (Gunners can do that), but it's definitely a good idea.
* By the rules, Overpowering Weapons and the use of the Double Fire program are not mutually exclusive. Personally, I would have rather seen Double Fire written up in a manner similar to Rapid Shot for vehicles, with two shots but both at a -2 attack penalty, but that's the D20 System nut in me. If you are looking for a home-grown solution to that one, I'd suggest making the Overpowering Weapon roll for each attack, increasing the -1 penalty per round to -1 penalty per shot. This is, of course, a House Rule, and subject to your own tastes, as you see fit.
You could also do a search on ship combat in the T20 section of these boards, and read some of the very interesting points that have been made, and suggestions for fixes.
Hope this helps clear a few things up for you,
Flynn