I ended up solving my problem here with a little helper function that takes my basicHttpRelayBinding and modifies it accordingly:
private static System.ServiceModel.Channels.Binding GetBinding(System.ServiceModel.Channels.Binding bIn)
{
var bOut = new CustomBinding(bIn);
var transportElement = bOut.Elements
.Find<HttpsRelayTransportBindingElement>();
transportElement.KeepAliveEnabled = false;
return bOut;
}