Netmaker may help with this. You configure an "Egress Gateway" to 0.0.0.0/0 as your internet VPN, inside of a Netmaker network of 10.10.0.0/24. We do our routing rules differently and it is meant to be compatible. However, I'm a bit surprised you have this issue with regular WireGuard, as it tends to be quite stable for this sort of setup in my experience.