The dilemma we face with API Management is being able to deploy the custom Developer Portal (customized through the APIM publisher portal UI) changes to each different environme
Yes, you can show the Iframe on the developer portal and that Iframe can be deployed on the azure and that page you can write your logic.
I did it one of the portals but there is only one problem the design problem and also the authentication problem you have to authenticate service every time you open the IFrame.
Git configuration is the only option but it doesn’t cover artifacts which created via CMS UI, the static content like such as welcome page, etc.
FYI, And the Git base solution requires that the instance becomes read-only (or locked to a single-user) during operation.
Please vote this wish in APIM
There is no API present at the moment to control these options. You best bet is git integration, but that might not be quite convenient.