Pathfinder explicitly calls out the rules on extradimensional spaces, noting that
A number of spells and magic items utilize extradimensional spaces, such as ... a handy haversack.... Such items do not function, however, inside another extradimensional space. ... For example, if a bag of holding is brought into a rope trick, the contents of the bag of holding become inaccessible until the bag of holding is taken outside the rope trick. The only exception to this is when a bag of holding and a portable hole interact, forming a rift to the Astral Plane, as noted in their descriptions.
The d20srd doesn't appear to have such a rule (except for the exception about horrible things if a bag of holding and portable hole interact with each other), so it's fuzzier.
That said, keeping a haversack in a haversack (or replacing either with a bag of holding) should be fine - the contents of the inner container aren't available until removed from the outer container, but nothing bad happens.
In either case, however, both the 3.5 and PF description of the Handy Haversack say
When the wearer reaches into it for a specific item, that item is always on top.
Since the description calls out "the wearer", I don't think you could pull an item from the inner haversack out with two move actions: after removing the inner haversack from the outer, you would be holding the inner haversack, not wearing it. Strictly, to take advantage of the move action to withdraw an item, you'd need to spend some time putting the inner haversack on (and, presumably, taking the outer one off, though their being slotless makes that odd).
Do note that Pathfinder added the Secure Paypack, which is a slight upgrade to the Haversack (it has two additional one-cubic-foot or 10-pound compartments, and some nifty fluff).
Also, note that Bags of Holding are less expensive per volume/weight than a Haversack. For things like "a cooking kit, animal feed, a climbing kit, and a tent", toss them in the BoH and don't worry about the extra time it takes to get the thing out (none of those are meaningfully usable in combat aside from the climbing kit, which is only useful if already donned).
That said, this GM frankly doesn't care that much about how much is in your haversack (nor do most that I've played with), especially if it's just being used for wands (though, note the Efficient Quiver; wands are basically arrow-sized, right?), potions, scrolls, cash, gems, and the like. In a campaign where I did care, I'd likely be extremely receptive to players simply buying a better Haversack if they cared that much about having instant access to that much stuff. ... then again, this GM is currently running a monk with a Secure Paypack, a Type 2 Bag of Holding, and a Portable Hole (carefully stored in not-the-paypack-or-BoH), so...