I definitely don't want to lie to potential future employers, is there a particular way I should handle any questions about the gap?
If they do: you took some time to relax after school.
Say you started or finished a couple of months earlier so it looks like a 3/6 months contract and tell employers that the contract wasn't renewed because they ran out of work, which is probably half true anyway.
You shouldn't lie but this is massaging the truth in your favor ;)
I have no problem leaving the job off the resume (“resumé” means “summary” not “comprehensive”). If asked you could say that you listed all experience that you felt was relavant. But personally I think it is a valuable thing to have listed.
However, I strongly discarded with the parents suggestions for “massaging” the resume. Those sugggestions are pure lying. There is a big difference about highlighting certain aspects of a career and stating things as fact which are not true.