Unfortunately, while it's technically "straightforward," it's still going to be painful.
You pretty much need to know how it was published and...honestly, everybody involved with production.
If it was published as part of a supplement, you probably have a leg up. Supplements, I believe, are considered periodicals and you look for them the same way you look for a comic. Check the periodical section of the Catalog of Copyright Entries for the right years--happily sorted by title, which you'd hopefully know--or use Ockerbloom's "first renewal" list.
You already know this, but for clarity, you want to check the renewals for the twenty-seventh through twenty-ninth years after publication, or the original copyright, if it's somehow different.
If not, then it was a "contribution to a periodical." Those carry the same kinds of copyrights as books, so they're in the main renewal section. There, things aren't as user friendly. What you're looking at is the renewals of many more things, sorted by copyright holder.
Remember I mentioned having the names of everybody involved? Any person or company COULD have become owner of the copyright and filed the renewal. Again, check the publication year plus twenty-seven, twenty-eight, and twenty-nine for each of the candidate owners.
The good news? When you eventually find something, strips are identified by date, so you'll see the renewal listing for something like "19Oct39" on the list. The earliest listed is the earliest with a renewal.
(Of course, you can go deeper into this at the Library of Congress, by checking the original copyright registrations to see if they're valid and/or if the entity filing the renewal had standing to do so. Renewal paperwork was processed by humans, and they occasionally let things through that shouldn't have. They also occasionally miss listing a renewal that's perfectly valid.)