Ok, so I got a technique similar to Burning Rangers working.
I'm doing like BR, letting the VDP1 rasterize the sprites, SCU DMA the frame buffer to work RAM, then SCU DMA it to VDP2 VRAM, but instead of swapping the frame buffers or clearing it, I'm actualy using an offscreen area of the frame buffer.
So I don't have that 16 ms latency that BR had (well, it's my understanding from reading the VDP1 technical manual), so the game can still hit 60 fps in some areas (there is an impact on framerate, but lower than what BR did).
I had to work around SGL to get these working as, obviously, SGL never planned the hardware to be used in such a way.
If anyone is wondering how to do it :
1) Set your NBG0 or NBG1 layer to bitmap, 16 bits, scale x up by 2.2, y by 2.
2) Modify your system clip command to allow a range from 0 to 511 for the x value. No need to modify y.
3) Each frame, use a local coordinate of 432, 56, write a custom draw command and use a scaled sprite (8x1, no preclipping (faster this way), using a VDP2 palette value of 0 with no transparent pixels). Leave if in vram if you aren't using SGL. Also use a clipping window (352 to 511, and 0 to 111)
4) For each loop in your game's logic, start by DMAing the frame buffer array to the NBG0/1 VRAM (I use bank A0) with a for loop (like y=0; y<112; y++) and send the array in work ram line by line using SCU direct DMA.
5) Write - using custom draw commands - sprites or polygons that you will need to scale them (multiply) by x:0.454545 and y:0.5 in screen space coordinates to an offscreen area. Either use SGL's windows (far) for the transparent sprites, or just send them far in your drawing list to make sure they get drawn first and, more importantly, make sure they are affected by the correct local coordinates command.
6) Some time before vblank, DMA the frame buffer to work ram using again a loop to skip the lines and data. If you want to be safe, you can use the VDP1 registers to make sure you got past all transparent objects before DMAing the data. It will pause the drawing, so be warned! Transfer only what you need and ASAP.
7) Vblank, go back to point 4.
Of course, it won't solve the sorting issues since your transparent objects will be on top of everything, so you can use a low-quality model of your avatar using again mask values (0) and send them to the offscreen area, sorting everything with the current draw commands. You would also need to either send polygons masking the walls and all to the offscreen area or use a more fancy no-overdraw technique (such as portals, BSP, etc.).