Why not try running the plank over a heat source (I use a hot air stripper), moving it constantly back and forth to prevent scalding, while at the same time, induce the bend you need into the plank. You need to work slowly and keep the wood moving, cos if it gets scalded it will splinter, but with practise and care I have found this to be a quick and effective way of bending planks.
That said, I have only done this with cedar, it may not work as well with mahogony.
Ian