The more you mention the situation you are in, the more it smells like you need to get out of the closet and into the datacenter!
Get cheap crap pipes, move yer shit into a colo cage somewhere. That comes with a 100Mbps or even a 1Gbps Cogent unmetered pipe out to the interwebs. Have both sites VPN into it using as best as you can. I would take me a Peplink, break out a VPN connection to the colo, then route all the HTTP/HTTPS traffic over the cheapest pipe I can find.
Price on pipes and such would probably equal out on onsite versus offsite for a colo cage. That's when you move into the fun of counting power costs, cooling costs, even equipment costs if you move to a leased managed hosting model versus owning equipment. Then you will get good savings there in the long run.
As long as you can let go of the control of the physical machine, you can make some serious inroads into better network management. Hell, have you thought about cloud services? Don't even need a location, just be in the clooooooooooooooooud!