IIRC the transferToImageBitmap path is efficient and doesn't necessarily copy anything. The APIs are designed to allow the ImageBitmap you get to be a reference to the GPU texture that is the backbuffer of the canvas, not a copy. When you transfer it to the main thread you are supposed to draw it using a ImageBitmapRenderingContext, which doesn't need to do an extra blit, it's just directly composited with the rest of the page, all staying on the GPU. In theory if it's a full screen canvas with no DOM on top the browser could even skip compositing entirely though I doubt that's implemented anywhere.
Of course there are probably a lot of ways to fall off the fast path. And I guess you are doing software rendering for GDI so you're not starting out with pixels on the GPU in the first place. I'm not sure what the best path is for you but I think you can probably make use of OffscreenCanvas in some way.