"The engineer specs 350 mcm for the run. With copper going through the roof I cant see why I shouldnt be able to run 300 thhn."

Because the engineer spec'd 350 and you bid 350. In my experience if I was to ask to run the 300 two things might happen.

1) (mostly likely) the engineer would stick with his original decision for the 350.

2) (not as likely) They might accept the 300 and ask for a deduct.

On engineered jobs the service conductors are often oversized. The increase in coppper prices is not the engineers problem, it's your's.

GJ