I'd like to hear what would you, as a main person in charge of production of planes, get to be built in those two countries. You can decide to undertake a license production of a complete plane and/or some other design at your preference.
The compatibility with stuff made (or about to be made) in UK and USA is important, along with suitability for mass production, simplicity, durability & good performance. Since the UK would be looking for your government's support (not just for those planes), you can use that to 'extract' a right to produce any piece of military hardware needed for your plane(s).
The task begins in 1st Jan 1938 in Canada, 1st Jan 1939 in Australia, the new plane(s) will be in combat units within 3 years. New Zealand can join down under