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I was able to figure this out and I have all working. Wireguard-selective-routing document linked in your post above has all the ingredients.

You need to enable GW on Site B under "WireGuard instance" --> advance mode -->  select disable route and input IP address for your GW. This could be any available IP from your tunnel subnet (see step 2)

On site A, create a new GW (use IP assigned on Site B). You need a few FW rules and NATing etc. Pretty much almost all the steps from this guide apply to side A. You can skip step 2 on-site A as this would only apply to site B (uni-directional) in your example. Step 9 - Configure routing, is also not not required.

I am in the boat as your configuration except I want to route all Internet traffic via the opposite sites.
Site A --> WireGuard VPN --> Site B WAN and Site B --> WireGuard VPN --> Site A WAN. My WG tunnel works and I can reach local hosts between both sides. However, I was unable to route traffic to the internet. I have spent and tried many different configurations and nothing seems to work yet.

Anyway, please post an update if you find a way to get this working.