You need 4 pips to weapons to fire continuously with all the lasers. What your saying about shields makes sense, but it doesn't correspond to practice. I've never lost more than a ring of my bi-weaves, so the arrangement and technique I use works fine. My original question should be rephrased to "How can I make my 7C biweave shields stronger".
Just for information and clarity, I'm not a beginner. I have about 8000 hours in the game with at least 2500 of those doing RES farming - in particular, experimenting and finding ways to optimise it. That's around 150,000 kills. I don't just fly around in the blue zone with 1:1:4 pips. 1:1:4 is probably what I use most of the time because the shields recharge very fast and the incoming fire isn't very strong. I adjust them like anybody else would according to circumstances, though it's not particularly necessay. Obviously 4 pips for ramming. Remember, this is RES farming, not PvP. The goal of the project is to make a newb -friendly battleship that can earn as much as possible.
The beam lasers are really important to keep the ship cool. I can't see that working with the cooling beam in the 3 slot for the reasons you mentioned. Again the theory is good, but you need the 4 weapons pips to keep the lasers going, not 3. In fact even 4 pips aren't enough, and I have pulse lasers in the class 4 slots, not bursts because bursts empty the capacitor 12.5% sooner from 8 second to 7 according to Inara. I had already tried that. The aim is not to survive a long battle, but to kill quickly and repeat as frequently as possible for as long as possible.
Also, I've been playing with an absolute newb regarding combat. He hasn't quite figured out how to use his pips, but he has had no problem at all using the exact build I mentioned above. Previously, he had prismatic shields, but had to keep leaving to recharge them.