Re "The rest of the group" --
"of the group" is a prepositional phrase and doesn't affect the number of the subject. This is a common point of confusion. The plural object is closer to the verb and can throw us off. I fall for it myself sometimes.
"rest" is a singular noun.
I know we're not supposed to distribute the style guide to outsider, but let's break the rules here -- one of the joys of making the rules for this sort of thing is that I can break them. :) You were talking about the style guide earlier, and this might give a taste of what's in one. (Yes, it was in there, on page 8 -- lots of agreement issues on pages 7-10 under A for Agreement.)
Agreement, Intervening Phrases
When considering the agreement of subject and verb, keep in mind that intervening phrases do not change the number of the subject.
CORRECT: The pyramid was spectacular.
CORRECT: The pyramid built by the cheerleaders was spectacular.
INCORRECT: The pyramid built by the cheerleaders were spectacular.
In all three examples, the subject is pyramid and is singular. The intervening phrase, “built by the cheerleaders,” contains a plural noun but does not change the number of the subject. The verb must remain singular.
Does that resolve it for you? If not, let me know. Jeepers, but this feels more like an email than a blog post.