I have had this rifle for a number of years but haven't worked on loading for it as the mold I have which makes a lovely original style heeled bullet was a bit too big for this particular rifle. The 360 No.5s are notoriously all over the place on bore dimensions.
My recent work on a load for my 360 2-1/4" got me thinking that a lighter paper patched .366" bullet could work in this rifle.
I swaged some 150gr bullets and loaded them over 16grs fff black powder.
They certainly look handsome.

They clocked at about 890fps which is off of original velocities but they shot well enough to hit a 2L bottle at 100yds.
There is room to compress a bit more powder in the case so will see how that works next.

You can just see the top of the bottle explode as the bullet hits the bank in this picture.