This sounds like a case where we should just change the syntax. If Betty is the maid it should be written:

    They went to Oregon with Betty [a maid], and a cook.

This is how I was taught. Use ( ) or -- -- here and the Oxford comma for list of 3 or more.

I get lazy with adding the comma before the "and" in list, and without fail I hear my grandmother/father/teachers pointing out how wrong I am for doing so. Same for my use of semicolons followed by "and" or "but".

I never realized the Oxford comma was even something up for debate.

(They (went (to Oregon) (with ((Betty (a maid)) and (a cook))))).

((That (is (the (most natural) syntax))) and ((all (of us)) (should (switch (to it))))).

Many years ago working on natural language to SQL, when we had ambiguities this is how we’d clarify things with the user (albeit with the minimal amount of brackets necessary).

It looks like you might have learned how to diagram a sentence as a youth