You call the restaurant and explain the reason, they would be super happy to mark as cancelled on Yelp, but still keep booked on their system: Yelp is not giving this service for free, but they charge a lot of money on each single reservation.
And hopefully realize to stop offering the service at all
You didn't pay a deposit for the seat, and everyone on the planet is near their cell phone or someone else's. We have two each, here. It's NOT like the news of a venue change won't reach everyone.
I know plenty of people like what you are describing (always near at least one phone), but they are still impossible to reach quickly. Even when they expect a call, they can have their phone in Do Not Disturb mode. Or they ran out of battery, and didn't think to turn it on after plugging it in. Most of the time I have no idea what the issue is.
Also, he might live in an area with few options. Specially on short notice. Maybe the closest alternative with a somewhat similar style is far away, so even if you can get a reservation , not everybody will be able to get there before dinner time.
Basically, when he says it's hard for him, maybe just trust that he knows his life better than you do.