I can see where this would be aggravating with loose parts. But aren't they normally easier to separate when the male connector is installed on the board, and the board installed - or in other words, fastened, or anchored - to the machine (or workbench, or whatever)? In that way the black header will be anchored by hundreds of pounds, so all your removal effort & force would apply to the white connector instead of displacing the black one with it, so you would have an easier time.

Moral being: you can probably still use the connectors, so long as you don't connect them "outside" the machine.

But stuck as you are with them loose, you may have to clamp just the base of the male part as hard as you can in a toothed vise to simulate the "machine anchor", then pry the female portion with a screwdriver.