Would it be possible to achieve a much wider field by sacrificing magnification?
Ideally, something along the lines of the old 6x Leica Amplivid, which had about 12 degrees field of view, but even lower power, with a correspondingly wider field.
For hawk watches, a wide field really helps and magnification is less critical, so 4x or 5x would be fine, ideally with a 15+ degrees field of view.
There is precedent for a 5x glass. Ross produced a large number of 5x air raid spotter binoculars which gave faithful service in WW2.