Looking at the Campaign Guide again, the actual core campaign rules are only about 60 pages long (Section 3), and 9 pages of that is the CSCR combat example -- so the rules aren't all that long.
I won't lie that some streamlining could be done and rules sections broken out for clarity and reference sake, but the rules themselves are not too horribly long, and most cover eventualities (as all rules systems do).
How the VBAM campaign system works, the only way you could boil things down to a lower page count would be to remove entire sections of rules, namely removing the Tech, Intel, the CSCR Strategic Combat Resolver, and Orbital Bombardment. Rip those out and the rules that are left are pretty minimal: Economics, Movement, Construction, Morale and maybe Ground Combat. In essence, you are one step away from just assigning each system a set per-turn resource generation value and going from there. Distilling the rules down to that point would fit them in about 10 pages, but it wouldn't be much of a game at that point (IMHO). It is easy enough to whip together something like that fast.
Looking at Sovereign Stars again, it looks like it is mainly a distilled version of Twilight Imperium, which means it is aiming more at being a boardgame flavor than a campaign system. Similar beast, but different end of the spectrum.
The criticism is good to hear, though. What it sounds like you were looking for in a game probably isn't even close to VBAM. As mentioned, VBAM is a much closer cousin to Starfire than it is to Sovereign Stars or some of the simpler campaign systems out there.
What it sounds like you are after is a one-page system kind of like this:
Movement
Either hex based movement at 1 per turn, or jump lane based with Major Lanes (2 per turn), Minor Lanes (1 per turn), or Restricted Lanes (1 per 2 turns).
Systems/Economics
Roll d6 x 50 and assign it to each new system. This is the amount of points the system generates each turn towards new purchases.
All units are purchased using these resource points on a 1:1 basis to their point value.
Shipyards/Construction
Fighters and atmospheric ships can be built on a planet without the need of a shipyard. Larger ships require a shipyard.
Each shipyard at a planet allows an empire to build either a fixed amount of points per turn, or based on the local economy. VBAM uses the latter. For that reason, set the construction capacity of the shipyard equal to its location's resource output (ex: a shipyard at a system that produces 100 points per turn can build 100 points worth of ships per turn).
More expensive purchases can be paid for over multiple turns.
Ground Combat
As with most simple campaign systems, the best solution in this case is to use the boarding rules as a basis and have players purchase "Troops" that fit 1 Troop per Troop Bay on an assault ship. Resolving ground combat is the same as boarding.
You could also then say that 1 Vehicle Bay allows a ship to load/unload 1 Troop per turn. That would make having assaults ships with lots of Vehicle Bays desirable.
Then you could add in other abilities for your other Starmada specific equipment and away you go! As a quick rundown of quick ideas for effects:
Cargo Bays -- You could always have resource point accumulate at a planet and have to be moved via Cargo Bays, with the number of points a ship can carry being equal to 10 x Hull (for when Cargo Bays are 50% of Hull) or 10 x Military Cargo Bays (when using 100SU Cargo Bays). From experience I would recommend against this, as it adds a lot of micromanagement. It adds some flair to the campaign, sure, but the micromanagement (oi).
Construction Bay -- Turns a ship into a mobile shipyard with a construction capacity rating of 25 times the number of Construction Bays. In Starmada scenarios involving normal shipyards, you can just use Shield 0, Engine 0 units of the appropriate Hull size and Construction Bay total to represent them in combat.
Is that closer to what you were looking for, Enpeze? It is certainly far simpler, and throws out most of the more complicated VBAM rules -- mainly because the above is an entirely different beast and is simplified for those that just want to play Starmada battles and really don't want the burden of managing an interstellar empire beyond what it has to do with generating that next Starmada battle.
-Tyrel