Good thought on the grinding Nathan. There are companies that use a large sander like what is used for wood flooring for leveling. Diamond coated disc and grinding would produce a more durable surface than fill type leveling. For more DIY, you can get smaller diameter diamond discs that fit on a small hand grinder. I've used this to get some areas level for door swing.
Lots of dust, but there are ways to make a shroud that connects to a shop vac to help.
