Now, I know you wanted to say was really .
OK - from the NEC (Article 100 - Definitions) : "Raceway - An enclosed channel of metal or nonmetallic materials ...". By definition, your wooden chase can't be a raceway.
BTW - if you're back to running a "40 amp subpanel, with a 40 amp breaker in it" - I'd ask your AHJ about that. They may give you grief about having a subpanel with a 100% load running off of it. If you have the 8/3, run a subpanel for the lighting and receptacles (you do need a convenience receptacle out by the A/C unit) and a separate 8/3 run straight to the A/C and a outdoor weatherproof disconnect switch (not a subpanel).