Ask yourself; are you waiting for your accuracy with your longbow to rival that of your compound, to be "confident" enough to hunt with a stickbow. If you are, it could be a LONG time before you feel "warm and fuzzy". I'm not saying stickbows are less accurate in the hands of the right archer, but you could be comparing apples and oranges. I like what Fred Eichler once said, "Don't hunt with a stickbow because you want to increase the challenge. Hunt with one because it's the most efficient weapon you can carry in the woods."
My advice, if you truly want to take a deer with your longbow, leave the compound in the case until you've taken a deer with it-- practicing or hunting. BTW, stumping is great practice, so keep it up.
Finally, I admire your patience and good judgment in knowing your limitations.