SMB3 doesn't work like SMB2. SMB2 scrolls the BG layers using the hardware registers while SMB3 always keeps BG1 fixed in hardware. So all 'scrolling' in SMB3 on that layer is done via regular tilemap/tiledata updates
Err, what? SNES SMB3 certainly does use the scroll registers. Simulating scrolling by redrawing the entire screen pixelwise every frame would be impossible without a coprocessor.
As for how the HUD is fixed in place in SMB3, it's done with an IRQ that rewrites the BG1 scroll registers on scanline 192... probably because that's how the NES version did it.
OP, are you trying to create a transparent HUD like SMB1 and SMW, or a fully opaque one like SMB3? If you want it to be transparent, you're probably going to have no choice but to use sprites. The thing is that SMB1 doesn't scroll vertically at all, and SMW only uses BG3 for graphics that don't scroll vertically, like the clouds outside the Ghost Houses, so in those games the HUD and the clouds never have to coexist on the same horizontal line. SMB2, on the other hand, uses BG3 for clouds everywhere, including the many areas that do
scroll vertically. So if you put a HUD on BG3 it won't be able to coexist with the clouds. The clouds will just have to abruptly disappear at the top or bottom of the screen (whichever side you put the HUD on) which kinda spoils the whole "transparency" effect.