The first and most important suggestion is to make sure your chisels are sharp and to sharpen them frequently.
Saw into the wood at intervals of about 3 inches, across the grain, almost down to the level marked on the wood. Then use your chisel as a wedge to split the excess wood off of the piece. This lets you clear away most of the unwanted wood quickly.
When gouging out the beam supports, drill through the support at the center of the curve with a large (11/4") bit. Use smaller bits to clear away more of the wood along the curve. Then use your chisel and mallet to cut through the thin walls between the drill holes. Trim up the surface with a chisel. When drilling or chiseling all the way to the bottom of a piece, have a piece of scrap wood below your work-piece. This helps prevent unwanted chipping. Also, when clearing out an area with your chisel, score the edges of the area (lightly notch the line) with the chisel, again to prevent chipping.
When chiseling along a curve which coincides with the wood grain, chisel down the curve, or across it, but not up the curve. This avoids serious splintering of the wood.
I used 2x4 ' s as the uprights, but did not wish them to look like store-bought 2x4' s. I chiseled and planed off the sharp edges to give the wood a more rough-hewn look to match the other hand-carved pieces. With a little practice, you will find that using the hand-saw and chisel to carve the loom pieces doesn't take very long at all!