Imagine a rocket that uses a mixture of liquid nitrogen and oxygen as the oxidiser.
It is designed like an oxidiser-rich staged-combustion engine, however there is so much nitrogen in the mixture that all the fuel can be burned in the pre-burner without the gas becoming so hot that it melts the oxidiser pump turbine. The pre-burner then, in effect, becomes the main combustion chamber, and there is no need for a combustion chamber downstream of the oxidiser pump. It may be that there is no need for regenerative cooling channels. The engine is used on very low staging-velocity boosters where high thrust to weight is more important than exhaust velocity in achieving greater efficiency.
How would such an engine be optimised (eg. expansion ratio, isp, pressure) to achieve maximum thrust to weight ratio and minimum production and development cost?
(It's okay for it to be as low perfomance ISP-wise as a steam rocket - though probably with far better mass fraction. Perhaps optimising some-way between the ARCA steam rocket CONCEPT (i.e. on paper not reality) and a conventional chemical rocket)