Well in that case, it looks like a 7806 or three would be a useful addition to your parts box. Since you have spare '05s though, perhaps it's worth trying with the laptop power. I'd be more inclined to find another wallwart - if you're anything like me, you'll have a plethora of them from long defunct devices. Alternatively, do you have any 7812s or similar to do a cooler two stage stepdown?