A practical approach is to use a printable lens-hood pattern and build a test hood from paper or cardboard first. If printed at 100% scale on the specified paper size, it will give you a properly sized template that you can test-fit and measure before making a more durable version.

For a 300mm lens, hood length is generally not very critical in terms of vignetting because the angle of view is very narrow. On full frame, a 300mm lens has roughly an 8° diagonal angle of view, so the hood would need to be extremely long—well over a foot—before it would start to vignette. That means you have a lot of freedom to make a deep hood as long as it mounts securely and doesn’t intrude into the frame.

So the best path is:

1. Print a hood template at true scale.
2. Test-fit it on the lens.
3. Measure that mock-up for diameter and length.
4. Rebuild it in a sturdier material if desired.

This is likely easier than finding exact factory dimensions for the original 39FH hood.