Sounds like you need an approved building inspector rather than your current one. Trouble is its difficult to switch halfway through a job.
Your BCO is WRONG if he turns down a solution involving tried and tested intumescent technology.
There is no problem whatsoever in using either Wee Brians suggestion of a fixed step or a proprietory upgrade provided the system is tested to BS476 and you follow the instructions. Intumescent veneer, paper varnish or paints are all fine on the right door with the correct application. See Sealmaster, Envirograph, English Heritage websites.
I would ask him to put the reasons for rejecting your proposed solution in writing and then write a letter of complaint to his boss. If that draws a blank then send it to one of the big companies- they may be interested in taking it on for you.