...has anyone ever done a breakdown of TOS VFX shots by effects house? I'm talking mainly space-based opticals: ship flybys, planets, weapons fire, etc.
I looked into it once regarding weapons fire.
Not surprisingly, in the first season several different effects houses were used (likely working relatively concurrently, so no time to compare notes), which is why everything was wildly inconsistent. I believe the footage of the eleven footer itself for "weapons firing angle" in the first season came from Howard Anderson, with the exception of The Alternative Factor, which I think was Film Effects of Hollywood.
The Corbomite Maneuver: Howard Anderson Company
Balance of Terror/Alternative Factor: Film Effects of Hollywood
Arena/Errand of Mercy: Westheimer Company (if online screencaps can be trusted, their "proximity phaser" in Errand seems to be slightly different from Film Effects version, it appears to be above the three lights on the bow of the saucer - I still need to verify this at some point; note the Trekplace link above says that Balance and Errand use the same shot, but accodring to Trekcore they're different)
Who Mourns for Adonais: Effects Unlimited (footage reused for The Apple, which was a Westheimer episode)
The Doomsday Machine: Cinema Research Corporation
The Changeling/Journey to Babel: Westheimer Company (reuse of Errand effect, but now a photon torpedo)
Obsession: Westheimer Company (iconic "Making of" phaser shot used for the rest of the series, I believe the eleven-footer footage was filmed by Film Effects, however)
Van Der Veer Photo Effects was the other optical company used, but none of their early season episode featured Enterprise firing weapons, they do get an honorable mention for The Tholian Web (although stock Westheimer footage was used for the phaser shots in that episode).
Use of these different effects houses is why the transporter and hand phaser effects are slightly different in various episodes as well.