I mentioned seven traffic tickets -- all for speeding -- from six states on my application and the very first thing I was asked -- after I took the oath -- was why I had been arrested! I calmly explained that I had not been arrested, just received citations. The officer was exceedingly friendly and constructive throughout and I never felt threatened, stressed or nervous in any way. It seemed like he had prioritized the list of "loose ends" to tie up during the interview and this was top on his list.
When I mentioned the citations he asked if I had them, which I did (I am a pack rat and had preserved every ticket dating back as far as 15 years!). He took the originals and added them to my file. He said it was good to have proof of resolution in the record, although from his tone it sounded like a "good-to-have" rather than a "must-have" but this is just the speculation of someone who did-have. I don't know what the situation would have been had I not had the tickets and proof-of-payment / defensive driving certificates.
If you go without the tickets, Imminfog, please write up your experience, as I know there are many in your situation, who would be eternally grateful to have a definitive answer on this stress-inducing topic. For a while, I was unable to find my ticket records and was in the same state of anxiety that I know you are in now. You have my sincere best wishes that all goes well!