Hello @Justin Nix,
Just sharing some initial thoughts, how about exploring the option of deploying Container Instances in a VNET
https://learn.microsoft.com/en-us/azure/container-instances/container-instances-vnet
Then that particular container in the VNET can communicate with on premise sql servers either through VPN Gateway (https://learn.microsoft.com/en-us/azure/vpn-gateway/vpn-gateway-about-vpngateways)
Or Azure Express Route: https://learn.microsoft.com/en-us/azure/expressroute/expressroute-introduction
Regards,
Shiva.