You do have some options. You keep the 36t on the rear wheel and run to a Strumey Archer S3X IGH that's being used as a jackshaft transmission. It'll be like having a 58t, 48t, 36t in the rear with this shifter bike build.
The other option is to have the engine 10t running to a double 20t on the left side of a jackshaft which then runs to the 44t+ rear wheel. On the right side of the jackshaft you can put a disc rotor. You'll have to weld nuts to the seat stays to be used as bosses to mount the brake caliper. You'll have to use a solid tensioner, it can't be spring loaded. Nor do I recommend using a rag-joint with this setup. Mount the rear sprocket to a disc brake hub.