Guess you're not interested in selling the pelts, eh?
Most guys worry about making two .24cal holes, you plan on making up to 41!
If it were my shotgun, I personally wouldn't use the extra-full turkey tubes with buckshot. It's possible it could damage the barrel, but I'd also guess the large amount of compression of the shot column would badly deform many of the pellets and blow the pattern. I'd try the Modified tube first and see how it does. I don't imagine you'd need too many hits to drop a coyote. I suppose the only way to find out if the #4 buck will pattern out of the turkey tubes is to try it (at your own risk). It's your shotgun.
Good luck,
Mike