I don't know Engl Screamer nor Behringer FCB1010 but I would go 4-cables method

Guitar -> 11R input
11R Fx Send -> Engl input
Engl Fx Send -> 11R Fx Return
11R output amp2 -> Engl Fx Return

Then I will connect:
FCB1010 midi out -> 11R midi in
FCB1010 switch1 out -> Engl clean/lead footswitch in

Set 11R "rig output no cab"

Create rigs in 11R and set 11R fx loop where you want to send 11R output to Engl input.

Create patches in FCB1010 to recall 11R rigs (midi 1-128) and set switch1 to control channel of Engl.