I have a “Root Slayer” shovel that I bought 2 years ago and everyone who uses it agrees that it is the best in hard soil. It is made to go through roots but works great for tough digging. As many have recommended it has a very sharp edge and is very narrow. It may be worth breaking up the soil with this shovel and going back with a wider shovel to move the rest of the dirt. This would probably be easier than a pick ax if you aren’t used to using one.
My other suggestion is to use the weather. I try and do most of my shoveling after a good rain of at all possible or the very least get my shoveling done before July.