Play this along with the attached lua script (see https://tasvideos.org/UserFiles/Info/637771986846795789). The script puts banjo in the correct position for bitclips Note the button file doesn't do furnace fun properly, but the youtube upload edited in a video of it done properly from one of my old projects.
Using the fall speed and a lag frame you can get through the stair. The ground is solid underneath and you can just jump into MMM. This saves about 2-3 minutes in 100% and 5-6 minutes in any%. It might possibly be PAL only, but I'm still looking into it.