As You can see, sometimes it does not do much investing 7, 8 or even 9 points in a particular skill that seems important.
If You are playing Ground STFs, a few points in Willpower (I for one put three points there) are a very good investment. Tachyon Harmonics depend largely on Particle Physics and Probability Logistics if memory serves: http://www.stowiki.org/Ability:_Tachyon_Harmonic
I am not sure which skillset to use with a Tholian Recluse Carrier, it largely depends on how You play that kind of ship, which weapons and consoles You use etc.
I did not play carrier-type ships for too long myself so I am not sure if a Quantum torpedo is a viable thing compared to an all-Beams setup and Beam Overload/Fire at Will.
Antiproton do profit most from Starship Targeting Systems and Starship Energy Weapons Specialization as these increase the critical range and damage. Of course, Starship Weapons Training will help as well.
I'd personally use beam arrays only with Beam Overload and an Attack Pattern (Omega or Beta) - and a low Fire at Will to get rid of pesky slow torpedoes and fighters or to draw attention to my ship. It would mean having to broadside a lot in my carrier.
On second thought:
As several of the more interesting Science-Skills require a front targeting arc, a torpedo weapon up front might be not too bad, either. Perhaps the Omega Adapted Borg set might be something for You - or the Romulan set. The latter one would compliment a change to Plasma Beam arrays, though.