Try to use Leadfoot and the electric fence to herd the Green Things into one area of the ship, so that when you do find an effective area effect weapon you can use it to wipe out many of them at once. No strategy is foolproof, as you could get particularly bad chit draws. But, if you test all of them fairly quickly, you can learn early that you are doomed and try to escape via life pod. Then you can start the next game that much sooner. The only meaningful strategy I have seen in this game is to test area effect weapons with wild enthusiam, starting with a fire extinguisher.
People often overlook the lifeboats in their planning.
A good crew strategy is to try to secure the lifeboat area and threaten to leave on all three ships. That means a possible crew strategy is to run for the boats, testing to see if they get a good area weapon. Closing off the boat areas is not an insurmountable task for the green things, but it is something they have to worry about. Oops, I mean the lifeboats. High damage area effect weapons are a must-have.