I don’t understand what you’re trying to express. I can’t make sense of what you’ve written.
If the Dan in your example used he/him pronouns and so did Steve, then it is equally unclear
“I was with Dan (he/him) and Steve (he/him) the other day. He hadn’t brought a poster he needed and went back to the car to get it.”
There’s no way to know whether the “he” is Dan or Steve. The they/them pronoun isn’t the problem in your example, the structure of the sentence is.
There’s no way to know whether the “he” is Dan or Steve.
Your example sentence is always ambiguous because there is only one sense of the word “he” but two possible objects. My example sentence is always ambiguous because there are two senses of the word “they”. The two situations are completely different linguistic issues.
Your example is of a poor speaker. My example is of a poor pronoun choice.
The they/them pronoun isn’t the problem in your example, the structure of the sentence is.
I disagree entirely.
Dan (or Steve, or both) is the subject of this sentence, not the object.
In both sentences, the pronoun used has two possible meanings in that context. That the two “they” definitions might be listed separately in a dictionary does not seem very important. It wouldn’t even need to be separate, as “third person pronoun, indeterminate number and gender” would accurately cover both cases.
What would be a non-ambiguous version of the sentence, in your opinion?