Hi @BlakeFullerton,
Assuming you build your integration using the latest LTI 1.3 standard, there isn't really an App Store for those integrations yet. The Eduappcenter, which manifests as the "Apps" tab in account or course settings, was built for the LTI 1.1 standard, and will probably fade away at some point as that standard is deprecated. Hopefully Instructure creates something for LTI 1.3 to at least list the apps, even if installation is not possible, but I don't believe anything like that exists for base Canvas LMS today.
The community here does have a partner listing page which some people may use. Do you have an entry there already? If not, I can try to find out how those are created for you.
-Chris