As a practical matter, most courts will not allow you to pay the fine for one charge if the traffic ticket contains multiple charges. As a legal matter, a double jeopardy analysis is conducted for an individual charge, not the case as a whole. Although the answer to your question is an easy "no", I like the fact that you asked the question and are seeking to use a novel defense. That's how case law is create and progress is made. If you're looking for some free information on OVI, the link below will help.
This answer is provided for informational purposes. It is not legal advice and does not create an attorney-client relationship.
I do not know the law in Ohio, but you do raise an interesting issue. Perhaps you should consult with the attorney who wrote what you mentioned. Double jeopardy is a very complex avenue of the law and it takes reading a vast number of cases and time to understand even for scholars. There are numerous US Supreme Court cases to read, and probably as many Ohio cases to read in order to get the gist of it. It rarely arises in the usual criminal case. The language surrounding the concept is itself quite confusing.
R. Jason de Groot, Esq. We do not have an attorney-client relationship. I am not your lawyer. The statements I make do not constitute legal advice. Any statements made by me are based upon the limited facts you have presented, and under the premise that you will consult with a local attorney. This is not an attempt to solicit business. This disclaimer is in addition to any disclaimers that this website has made. I am only licensed in Florida.