Then if you treat them as root position F chords things get even worse. It makes me think of Johnny Depp and nobody wants that. This is what a lot of covers do, I've noticed.

This is what bars 7 and 15 sound like if we do treat them as F/C chords, things start to sound too Pirates of the Caribbeansy.

If you have a bunch of moving parts and what the chord is becomes unclear, play a powerchord of what you think the chord is, and if it fits it sits. In bar 7 and 15 I'd argue the C powerchords fit under what are harmonised non-chord notes that resolve to chord notes.

Terminator 2 adds a countermelody. In bar 7 now the melody note A is harmonised with an F. Bar 15 has the F melody note harmonised with an A. It's easy to see this and think the chord in both cases is an F/C. But it is not because of what we know of the original and because of the 'powerchord test'

The first film is just bass note and melody. If you listen to bar 7 it is clearly a C chord that has a non-chord note A (the 6th) resolving to a chord note G (the 5th) in the next bar.
Bar 15 is a Csus4 with the F (4th) resolving to E (3rd) in the next bar. This is crucial for what's to come.

Saw Crash the other day and became obsessed with the score, it's probably one my favourite Howard Shore Cronenberg scores, up there with The Brood. I started transcribing it, there's some cool guitar parts.