I've used my SAK saw to prune limbs up to @ 2" in diameter, but as you say it was testing the limits of the saw. Your list is adequate but limited. The Silky will work well on the bamboo but you will probably end up cutting around the circumference like you do with your SAK saw. But, your machete or ax should work with the bamboo so the smaller saw can be used for more delicate tasks. My only concern would be sharpening the saw when it dulls (therefore, multiple blades).
Your machete is plenty strong enough for splitting the bamboo. Although, for 9" bamboo I'd get a longer machete. You want to use the belly of the blade for splitting and leave plenty of the blade to baton on towards the tip.