Is it possible to access my outbox to search for a comment I made?
I've tried searching my inbox for the conversation I'm looking for, but it hasn't helped.
Yes. On your profile, first go to the "activities" tab and then choose the "comments" sub-tab. This will show you a date-ordered list of comments you've posted that have not been deleted. (Like deleted posts, deleted comments don't show up on your profile.)
If you've never looked around in "activities" (used to be called "activity") before, check it out -- all your posts, reviews, edits, and more are there.