On the board bows I've made, I started with a 3/4" board, which is way thicker than I will end up with. I glued on another section of 3/4 board for the handle. Then I carved out the fades, continuing the slope of the fades into the main board. The limbs then get taken down to 3/8 or 5/8 or whatever thickness, but slope up to 3/4" before the glue line of the handle. This way, the bow would be stiff in the middle even without the handle piece.
Where you would run into trouble is if the main board is thin enough to bend during the draw (might happen with 3/4" on a heavy bow), and you glue a thick, stiff riser onto it. You could deal with that by using a power lam of some sort, which is thin enough to bend and runs a few inches beyond the handle on either side, adding depth to the limbs and making them stiff through the handle section. Or maybe you could build the handle out of several thin laminations, each thin enough to bend.
Poplar should be fine in a stiff handled design, but it might need to be a hair thicker and wider than other woods.
