Calling the puffs upwind is pretty easy, but downwind I find it somewhat more challenging. I'm definitely working on getting better at it, but I'm happy to use the traveller to cut down the amount of swimming I have to do while I learn.
When the traveller is dropped, I'm letting more air spill off the leech of the mainsail, reducing heeling motion, right? In addition to this, since the main isn't generating as much force on the boat any more, am I also moving the center of effort for the boat forward? Would this result in more lee helm, and help the boat bear off?
If you find it difficult to know which direction the puffs are coming from, you might want to put some yarn on the side stays. They will point to the direction that the puffs come from.
You have the effect of letting out the traveler ocrrect. One thing that use missed though is that you will be closing the slot between the spin and main. Although more dangerous, in theory, letting out mainsheet (don't drop it!) should be faster because it twists off the top and flattens the spin by decreasing the luff tension.
If it is gusty, you may not be able to react fast enough on the mainsheet because it requires you to let out and pull in a lot of rope.
I found that weight distribution makes a big difference. Getting the crew on the trap makes the hull come up slower. It also makes turning down more effective because you are going faster and have a higher center of gravity. if you can get the crew to crouch in lulls and stretch out in puffs, you can control the puffs better too.