Let's go back to the 5000 ton ship with 150 lasers for a minute. There is a way to handle it without making too many rolls.
First, weapons of the same type (beam laser, pulse laser, missile rack) in a turret fire linked, not individually. Three give a +2 to hit and allows two damage rolls. Two give a +1 to hit and allows one damage roll (one gives no bonus and allows one damage roll).
Next, determine how many turrets of the same type and armament are firing at the target. There is an additional to hit bonus equal to the square root of the number of turrets committed, minus one (sqrt(# turrets)-1). The number of damage rolls from the first step is multiplied by the number of turrets firing.
So, in the example above, the ship is firing 50 triple laser turrets. A triple laser turret is worth a +2 to hit and 2 damage rolls. Fifty turrets give an additional +6 to hit (+8 total) and x50 damage rolls (100 rolls total).
At the referee's option, a single damage roll can represent up to ten hits, simply increase the damage to the location rolled.
So, the 150 lasers can be reduced to one to hit roll and as few as ten damage rolls.
How about just dealing with each pip as it's 9% chance, no range adjustment is short range, -2 is medium range and -5 is long range, die roll +/- range/gunner/sand/computer or program DMs, multiply 2d6-1 result x .09 x potential hits.
So with a normal range of rolls, one could get 9-99%. With negative DMs, some low rolls at range or other negative DMs may not hit at all.
Example roll 7, no DMs.
7 x .09 = .63
.63 x 150 = 94.5 or 94 hits.
At medium .45 x 150 = 67 hits, long .18 x 150= 27 hits
That''s an extreme example of handling all 150 hits on one roll. I would expect grouping shots by DM mods, most notably gunner skill.
Additional thoughts to HGize CT-
Mounting bays are as per HG limits.
In addition, for EP-rated bays or screens the power plant must be a rating higher then the M-drive per bay- if power damage drops to even or below the current M-drive, the bay(s) cannot fire and the screens cannot protect (alternatively the drive can be used at a lower rating freeing up power for the bays/screens).
To determine damage from powered bays, the weapons factor is multiplied x5, and PA and Meson Guns deliver x5 factor in radiation hits using the radiation table from SS3. The 2d6 roll is then performed, DMs applied and damage determined as per above.
Missile bays are 150 missiles for 50-ton bays and 300 missiles for 100-ton bays, typically fired in 5-missile salvos if resolving missile by missile. Or if by bay, x5 per missile factor, x10 if nuclear plus x10 radiation, multiplied by the die roll +/- DMs.
The advantage of a missile bay is continuing firing, the now-empty part can start reloading from a magazine while the bay continues launching from full cells.
Anti-missile shots against incoming missiles are resolved on the hit +/- DMs x potential hits of lasers/energy weapons system.
NDs resolve individual nukes on 3+, otherwise die roll x ND factor x 5 and subtract from nuclear hit total.
Meson Screens subtract 100 + factor hits to Meson Gun hits.
All weapons use the 1977 damage table except for Meson Guns and nuclear weapons, which use the 1981 table (in other words MGs and nukes can get critical hits, the others cannot).
For high number of hit resolves, simply roll damage as normal and apply 5 hits per roll. This should get some randomized results while speeding resolution.
Energy weapons cannot fire on targets past short range, and fire with a +2 DM.
Meson guns get +2 on targets at short range, and -1 DM for every potential G the target ship is NOT using for acceleration.
Armor rating is resolved by rolling 1d6 per armor rating, that number of hits may be changed to fuel hits.
I feel pretty confident that I don't have all the ratios exactly right, but this sort of thing could be the starting point of making something workable.