After digging around in the IMapper interface (and thanks to the documentation link provided by @LucianBargaoanu), I found exactly what I needed.
In ConfigureServices():
// Adds AutoMapper to DI configuration and automagically scans the
// current assembly for any classes that inherit Profile
// and registers their configuration in AutoMapper
services.AddAutoMapper();
The secret sauce is to add IMapper mapper as a parameter to Configure() – the parameter list is dependency-injected so you can reference any service registered in ConfigureServices()
public void Configure(IApplicationBuilder app, ... , IMapper mapper)
{
...
mapper.ConfigurationProvider.AssertConfigurationIsValid();
}
Works exactly as expected.