Big-IP in Azure with thousands of domains

Let me describe our configuration, we have a few thousand custom domains pointed at what looks like a single IIS instance. It's well beyond what Microsoft recommends but it works. As all of our remaining infrastructure is in Azure we wish to migrate there, but none of the Azure services (App Service, Front End, Traffic Manager) support the number of custom domains we currently have in a single service.

In my experience with F5 within the airline industry I know a physical F5 could handle the routing and SSL description of the number of domains in question. I haven't looked for a few years but while the virtual F5 could do it on a properly scaled VM there were limts on it.

That means the question of the hour is can I create a F5 VM "service" in Azure that could service several thousand URLs along with their SSL decoding and route the traffic to the appropriate back-end Azure App Service which would know what to serve up based on the HTML header.