What ropes size?????

[Paul201t]

I currently climb on a 13mm marlow with a 10mm eye2eye distel hitch with pulley. I was going to get a petzl zigzag but because of the 2 main line working at height regulation I’m put off with having the cost and having 2 clunky zigzags knocking about. I was going to get thinner 11.7mm stein rope for the zigzag for smoother running. I still want to get thinner diameter rope as it’s a lot lighter and manageable. Was wonder if anyone knows how a 10mm distel hitch performs on a 11.7mm line. If at all? I done loads of research on what works best for zigzags but this 2 main line thing has put me right off. I work well with distel hitch so will stick with that now I got to get use to working two main lines.