Unfortunately I've removed many of these for boiler, cooling tower and chiller work. They never are easy access locations. Here are some tricks that may help make your job easier:
The dent on the back is probably the set-screw, HR-Veedu. Often they are hex head (Allen) screws. Perhaps try some Allen wrenches to see if you have good luck.
Bad luck is that the screw was a break-off type used in commercial applications and is broken. If so, can you fit a drill in to drill or use an easy-out? (No such luck, right?)
Any luck that the hose bibb is NPT so you can spin it off for easier access on the workbench?
OR-
Looking at the saw cut in the 3rd photo, you're pretty deep. Maybe make another cut just as deep 180 degrees away. Then use some water pump pliers, like Channellock 420's, to turn the fitting. It'll peel apart. (Those are made with soft, yellow brass.)
OR-
Make another cut at an angle and have the bottoms of the two cuts meet. When you turn with pliers, the wedge you just made will fall out. Tapping the side of the wedge gently with a dull chisel will spin the body off.
A Dremel with a cut off wheel might help you cut faster & with easier access, too. (Good excuse to buy a Dremel)
A large Nut Splitter will crack the body in half without damaging the hose bibb threads. You'll have to shop on line for a large enough one with a wide chisel that won't break the bank. Those at plumbing suppliers are really expensive.
For the replacement, I suggest a stainless steel screw with anti-seize paste. Leave the head sticking out so you can grab it with pliers. (Or skip the vacuum breaker if you can get away with it.)
Best Of Luck & Let Us Know How It Goes!
Paul