I can't answer the left/right question. I don't hunt in Washington and I'm not familar with their regulations, but I assume the regulation is there to prevent the use of sabots. The maxi-ball and maxi-hunter should be perfectly legal.

I have some experience with the left/right thing. My caplock is a Thompson Center Renegade, right hand. My flintlock is a Lyman Great Plains left hand.
Normally you will have no problems shooting a right handed caplock, lefthanded. The only time I have ever noticed any blowback at all was with full loads of 120 Grains of 2fg. The Deerstalker probably maxes out at 100 grains 2fg.
The flinlock is a different story. Here you have exploding powder right in your face, and, probably more dangerous, tiny fragments of flint chipping off and molten slag from your frizzen, all right in front of your aiming eye. For these reasons I can only recommend shooting a lefthand flinter if you are lefthanded.
With either one it will help your shooting and be safer to use safety glasses. Especially while firing multiple shots during practice.