You know, of course, virtually all contracts are written and interpreted by lawyers. It is a specialty in the practice of law and a testing segment on the bar exam. Legalese itself defines this process as "contract law" and the person writing the contract, as a "business attorney." I have never come across any "title" beside lawyer, attorney, barrister, etc.
I think you're going to have to make up a word, like the aforementioned, 'contractology.' Of course, I am being facetious, "inventing" words, especially regarding a profession not your own, can be fraught with misunderstanding.
Use the existing terms for clarity.