i think the possible meanings are:
- Mr. Tanaka was appointed by the chairman to be the president.
- Mr. Tanaka was appointed by the president to be the chairman.
Is that all correct?
Using the idea in this thread The grammar of “虎から食べられた” and “虎に食べられた”? is maybe this a possible remedy:
making it unambiguous and meaning
Mr. Tanaka was appointed to be the chairman by the president.
Does changing "に" to "から" both sound natural and remove ambiguity?