Profit is literally the top objective of a For Profit company and they will charge the maximum they can get away with independently of taxes because that maximizes profit.

If as per your theory a company charges X because it pays lower corporate taxes, and when the taxes it pays go up it starts charging X + Y, that means it could've been charging X + Y all along (as in that theory of yours people clearly are willing to pay it) but didn't, so logically it was not maximizing profits. which goes against the very objective of a company.

In financial and accounting terms corporate taxes are not costs (they apply to profits only and can never make a profitable company become unprofitable) and hence don't cause the same effect on prices as actual cost increases which can push prices up because they force all market participants to do so as otherwise they risk losing money.

Ditto on your whole lowering of costs "theory" - if a company can already lower costs and is not doing it, then it is literally refraining from maximizing profits, so going against its reason of being.

You assume a causal relation that isn't there because the driving motivation for any company is profit maximization and all those things you say they would start doing if taxes went up they have an obligation of doing it right now as that maximizes profits and if they're not doing it that's because they can't, and there is no logical explanation for not being able to do it now because their taxes are lower.