If you use CONNECT, yet want to apply remaps, it'll modify the scheme. This seems to mess up various things internally, such that the requests are not properly tunneled. It seems nonsensical to allow medications to the scheme (since the client expects e.g. HTTPS, mapping it to anything else would likely make the client misbehave). This would be the easiest solution, and makes internal states (debug, logging etc.) behave as expected.
The other option is make the scheme irrelevant to the "core", but not sure what other side effects that might have ?