DownloadRedirect

I'm looking for suggestions on how to improve on my current design for testing a class (example below) that depends on HttpClient with a custom HttpClientHandler configuration. I normally use constructor injection to inject a HttpClient that is consistent across the application, however because this is in a class library I can't rely on the consumers of the library to set up the HttpClientHandler correctly.

For testing I follow the standard approach of replacing HttpClientHandler in the HttpClient constructor. Because I can't rely on the consumer of the library to inject a valid HttpClient I'm not putting this in a public constructor, instead I'm using a private constructor with an internal static method (CreateWithCustomHttpClient()) to create it. The intent behind this is:

• Private constructor should not be called by a dependency injection library automatically. I'm aware that if I made it public/internal then some DI libraries that had a HttpClient already registered would call that constructor.
• Internal static method can be called by a unit testing library using InternalsVisibleToAttribute

This setup seems quite complex to me and I'm hoping someone might be able to suggest an improvement, I am however aware that this could be quite subjective so if there are any established patterns or design rules to follow in this case I would really appreciate hearing about them.

I've included the DownloadSomethingAsync() method just to demonstrate why the non-standard configuration is required for HttpClientHandler. The default is for redirect responses to automatically redirect internally without returning the response, I need the redirect response so that I can wrap it in a class that report progress on the download (the functionality of that is not relevant to this question).