Monochrome:

I'd been considering this myself for some time now, and my tentative idea is to remove the icons entirely.

They add no value whatsoever since you're already hovering your cursor over an icon! In the best case scenario, you see two redundant icons:

In the worst-case secnario, the icons don't match, as you've written about here:

Since the "fix" for non-matching icons results in redundancy, I feel like we should just remove the icon entirely. It would reduce the visual noise in the tooltip and solve this entire class of bugs automatically.

+1 to removing excess icons