Parallel TRIAC's for greater heat dissipation
There is no benefit for you to paralleling triacs. Using two devices crammed into the same space as a single unit (with no heat sink) will destroy itself only a bit slower than a single triac. 

Triacs have a heat loss in the 1W/A (rms) region, and if you have only a few cubic inches you'll need to find a way to get the ~20W out of there while keeping the junction temperature reasonably low. This is really a non-negotiable requirement. Maybe you can put a heat pipe in there and connect it to a heat sink elsewhere. Use a smallish heat sink and a monster fan (and realize when the fan dies, so does the triac). Or liquid cooling. Or find a manufacturer (Fujitsu makes some, but not sure they cover 20A) that makes a low-audible-noise relay.