Remember the burner is capable of 90,000 btuh input, the stove is generally 86% efficient or so with respect to output for hot air, which it is designed for, that provides a net output of 77,400 btuh. With your coil only getting part of that I would estimate the net to the coil is around 45,000 btuh at peak burn.
One idea is that you need the coil closer to the grate, also you didn't mention where it crosses the grate, is it in the sweet spot where it gets flames all the time?
One more idea, when trying to heat a boiler with a coal stove that is regulating output based on air temperature and has no idea what the boiler needs I would expect that the boiler would fire a fair amount of the time.
Not sure if I have been helpful but best wishes for a successful science project.