What you're proposing is an inter-store R&R. I've never done it, but having done a lot of price checking in several stores, I think that HD is taking steps to prevent your ability to do that sort of thing.
The Night of the Long Nails -- and maybe reading of this thread -- has raised HD's awareness of some holes in their computer system, and from what I can tell they've been taking efforts to close these loopholes. At least that's what I see in terms of changed web site behavior and in terms of computer price checks in my area. YMMV.
It looks like they've made some significant changes to how the closeout SKUs are handled, specifically to put an end to some of the R&R tactics that have been popularized in this thread. It looks like they're changing the persistence of active SKU so that instead of lingering in the computer as an active SKU with a closeout price, they're quickly updating them so sold-out SKU have a near zero lifespan once INV=0. Once the SKU goes inactive it could be tough to do the interstore R&R, because the last store on your trip will no longer have the item in the computer at the discounted price. The progression seems to be that when a closeout SKU sells out, the SKU now quickly transitions to an inactive SKU, and later becomes reactivated at the normal selling price. It seems as if this change has been implemented specifically to prevent interstore R&R.
Take the Dewalt toolboxes for example. Last week I bagged several of them, clearing out what was in my area. I subsequently found other stores that had plenty of them in inventory at full price. But the stores where I had previously bought at a closeout quickly changed to inactive SKU status. It seems that this would make R&R difficult or complicated to do because the item is no longer in the store's system at a clearance price. Once the computer gives the SKU normal pricing R&R becomes impossible.
I haven't tried interstore R&R. They way HD is handling the closeouts, one store at a time, they intend for the closeout deals to go to many local HD customers in every area. They're deactivating SKUs after the store sells out to discourage the people who try to buy in one store and return in another, thereby concentrating the deals around a select few customers near one particular store.
I can't say that this is a system-wide occurrence, it's just what I've been observing in my area. It certainly makes sense from a business standpoint to tweak the system so that closeout deals are enjoyed by as many customers as possible, rather than a select few who are trying to manipulate the system.