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My last ship is similar to your. i have 10 shields point and 13.000 mass, but i try to build a very confortable ship with more space for all.
I'm not sure, so don't hold me to it too much, but I think I read one of the devs say no matter how big you change your ship you can only have ten stabilizers. Ship system points are limited by that, so you may not be able to throw on an extra ten shields.
You'll have to build smaller or live with weak shields. Or split your ship into smaller ships. Of course that leads to it's own set of logistics/personnel issues.
Also it's very counterintuitive, since in general larger objects (ships, tanks, etc.) are easier to protect due to the square-cube law - if larger shield generators generate stronger shields proportionate to their mass, and stress on the shields rises proportionately to surface area, doubling the linear size should lead to doubling of the shield strength. Many people may not be able to articulate the square-cube law, but intuitively everyone expects that larger vehicles or creatures can get better protection. It's the "propulsion" that typically limits size, not protection.
Edit: and having just looked at it, a 1x1 ship, with 1 stab, has around 70 hull points. a 2x3 ship with 6 stabs has... 156. Running it out with math, that means 6 1x1 ships, with a total HP pool of 420, will spend 4 system points each on engine (1), power node(2), and a generator(1) for a total of 24 out of 66 available, and have 7 free each for shields and weapons, for a total of 42 free points on weapons and shields- and keeping in mind each only needs 1 large shield to match 2-3 on a big ship.