I think I have a solution (well, perhaps merely an idea) to the apparent lack of projectile weaponry and prevalence of beam weapons that seems to be developing in some tournaments, whilst also solving issues related to aegis rules and lancets at the same time.
As well as a small increase in point defence pricing, how about the unlimited use of Aegis? However, Aegised sections are limited to 50HP, and can't have anything mounted on them. They are of course still restricted to sections per aegis limits, as well as a hefty price.
With a bit of testing, I think this solution works quite well. What it means is that beam-only ships can't touch a ship with 360 Aegis but that even if you add a bunch of flak a ship with a bunch of Gat Blasters can still take you down.
A variation on this is that you can have multiple generators target a single section, each of which allowing 50HP (so that a section targeted by three generators would have 150HP). Hopefully point limits and section limits would be sufficient to prohibit too much abuse of this.
A quick think about point defence pricing also leads me to believe that a scaling price might be appropriate. The first PD of a type you buy costs you 1 point, then the next 2, then the next 3 and so on. Therefore, if you wanted 4 flak, you'd have to pay a total of 10 points. 4 flak and 2 point beams? 13 points. You want to stop all projectiles with 8 flak cannons? That'll be 36 points please.
This should encourage lots of different types of PD whilst also putting a practical limit on how much you can afford.
Beamers aren't that good. The only reason you see them so much is that we've had about 3 seperate fleet tournements. Beamers are great in fleet tournements. They are even better in low HP tournements.
Fleet tourneys show how devastating a good firing solution on a unshielded section is. Beams become prefered because your ships won't be staring at the front deflectored section of a ship all day long and become a guarenteed hit. Combine that with low HP and beams become monsterous. Only a combination of ablative + lots of deflectors can stop them or ships with high speed.
In single combat, however, beams usually can't hit a vunerable area or fire frequently enough to do any decent amount of damage. You have to become creative with weapons.
The main point I guess I'm trying to communicate is that there are a variety of factors that factor into defacto beam dominance. The most important one is the ability to move to fire on an unprotected section. With projectiles, this isn't an issue. The only way you can achieve a similar effect is to hit a ship from two different directions with projectiles to punch past PD. With beams, if a ship can get a firing solution on an undeflectored section with the deflectors already set, then its almost a guarenteed section kill.
I've been wanting to propose a Aegis sort of thing that you've proposed for a while so tournements can have them. My idea was for any section with an Aegis shield to have its total health set to 10% of what it was. I like your idea of multi-aegis to increase the aegis cap. The only thing now is that is it worth the same as a deflector or still more? What about lancets?
However, I don't think that they are the solution to mass beams. The easiest way to achieve balancing beams is for fleet tournements to set them one point higher(assuming 100 point) and make section HP average to higher.