Some comments:
In the interpretations of beta_3 and beta_4, you don't need age fixed at that particular value; it just has to be fixed at the some value.
Similarly, in the interpretation of beta_5, you don't need C = 0, just rather C held fixed.
"...if interactions were not significant, I suppose I should use a simpler model, with a single C column which would still contain values centred within subgroup?"
The models are equivalent regardless of how you center C. Though interpretations of contrasts would change.
Contrasts:
#4 [F] [0 0 -1 1 0]
---You could just as well use [F] [0 0 1 -1 0] ; overall sign doesn't matter for F-test
#6 [F] [0 0 -1 -1 0] Average decrease in response in Groups A and B with increasing C.
---No. Rather, it tests whether the average response in A and B (with changing C) is significantly different from zero (intuitively, large in absolute value). And again the oversign doesn't matter; you could just as well use 6 [F] [0 0 1 1 0].
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