Looking at the diagram, I believe you want a basin wrench. It's designed exactly for these bolts in these tight conditions. And the next time you go to replace a sink, you'll be glad to already own one. That said, I've never heard of, nor seen a jaw dropper plumbing wrench, so I was hoping that someone with more plumbing experience would chime in.
Per Tester101's answer a bit more information
There are two main types of valves - washer and cartridge. In the washer type, the stem of the valve (the part topped by the handle) moves up and down on a thread. It has a washer at the bottom that, when closed, presses agaisnt the seat of the valve stopping the water. The higher the stem raises the washer, the more water that flows.
In a cartridge type faucet, the stem twists without rising. The water flows through holes in the cartidge and the body of the valve. The more the holes are aligned, the more water flows.
It sounds like you have a washer type. The tension on the stem, which controls how easy it is to turn, is usually controlled by a large nutlike cap that fits over most of the stem. The thin shaft of the stem comes through a hole in the center of this cap. The cap can usually be adjusted by tightening and this should make the stem slightly harder to turn. It should also prevent the stem from turning on its own due to water pressure. Tighten the cap by turning it clockwise a very small amount.
Occasionally water temperature can change as the washer heats up or cools down. This is usually found on much older washers and faucets, but can often be fixed by opening the stem and changing to a modern washer.
Best Answer
Probably.
Will it look good? Maybe.
Some single hole kitchen faucets have an escutcheon plate that will cover a standard 8 inch, 3 hole to allow you you mount a single hole.