Correct—the font licenses were a one-time cost. Previously, I was using Typekit, but I hit an issue with the requests stalling for ~3 seconds. Apparently, Chrome has a threshold of not loading more than ~5 requests from a single external location at once, which resulted in the stall. I reached out to the font foundries and they were incredibly helpful in letting me try out the fonts for performance testing. When loaded from my own CDN, they loaded instantly. At the time, I had some extra cash from a freelance gig I just wrapped up, so I went for the font licenses. To me, as the designer/developer/one-man-team, it was important to have design I intended for Cushion along with good performance—and supporting the font designers who were so helpful.

I think the limit for Chrome is a bit higher - 6 or so resources from the same location will cause the stall. You can usually see this happening if you watch the "Resources" tab in Chrome Dev Tools and watch the timings for loading each resource.

Are you allowed to use these fonts in a native mobile app?

Unfortunately, no—that's a different license, which is strangely much more expensive than a web license.