This really sounds more like an issue with the selected metering mode and not using exposure compensation. But there’s a half dozen ways to do most things; so…
Re-enable focus on the shutter button and set the AE/AF-L button to AE-L only.
The only back button focus function/capability you will loose is manual focus; but there is a switch on the body for that, and most lenses also have a switch and/or manual override capability.
Do as you normally do using BBF. Then when you encounter this situation point it at the grass, press the AE-L button, and use the shutter button to refocus.