I have to agree with Span Star. If you are getting paid to teach a certain way then that is your obligation as a part of that particular institution, then you should teach their doctrine. Since you did not disclose to the person hiring you that you are a Baptist, I think you may want to consider what is going through the person's mind that hired you. Probably why did this person not tell me this in the first place.
Or consider you are the hiring person for a Baptist organization, would you hire a Catholic to teach your children?
An under cover agent of God is an interesting idea, however, for messenger God to be a messenger, that person has to deliver the message with out compromise. Just like if some one was given a letter to give to another person, if they change the letter then the letter becomes invalid.
If you were outside of the school and not teaching there, then debate with who ever you want to debate, priest, imam, devotee, guru etc. I would just consider time place and circumstance.