Your understanding of the rule is correct. When two nouns, pronouns or noun phrases are joined by oror either...or, the number of the verb is generally determined by the number of the last noun or noun phrase. This is another example of attraction rule (= the verb tends to agree with a noun or pronoun or noun phrase that closely precedes it.)
Either the workers or the director is to blame for the disruption.
Either the director or the workers are to blame for the disruption.
Quite often, as you also point out, such sentences are awkward. A good way to avoid such concord problems is to use a modal auxiliary verb (which has the same from in the singular and the plural), for example:
Either the workers or the director must be blamed for the disruption.
The analysis here is based mainly on Geoffrey Leech and Jan Svartvik, A communicative grammar of English, second edition (1994), Longman