What strikes me first t is the constant battle speaking from this article, instead of a desire to achieve the best for a company by collaboration between departments. The second thing which strikes me is the mentioning of the CTO as ‘she’. Since most are still male in this industry I can only assume you have a particular individual in mind when you wrote this.

Two comments about the ‘four common objection phases’ you mention.
The ‘Surface completely logical and “obvious” objections’ phase is not a variation of ignoring the request. It is due to experience of a CTO that even though the question is logical and obvious, it quite often has not been considered by Marketing. By not considering basic question you set the entire project up for failure and the CTO is helping you to prevent that.
This sentence really struck me: ‘We want to be the people who are helping the CTO get her job done and learn something about herself in the process’.
It speaks of such immense arrogance that you as marketing guru are by definition far smarter than the CTO that I can see the projects getting a cold shoulder.

Perhaps that is the true lesson for you here. A little modesty can go a long way. If you really want to get a CTO to help you consider this:
1) Just like a boy scout, be prepared.
2) Get help from IT early on. Nothing is worse than being presented with a done deal project which you can rip apart by asking basic and obvious questions in 5 minutes. That’s just wasting time.
3) CTO’s are almost by definition Beta people, accustomed to logical thinking. Convince him or her about the benefits of the project for the company versus the cost.
4) As marketing guru you should know this better than anyone. You catch more flies with honey than with vinegar. Get on IT’s good side and see how helpful they can be.