Why not use more 1/16" shock cord for the door tie outs? That works pretty well.
The 1.2mm Tech Line from DIY Gear Supply
would work well for your side pull outs. I started using this all-round on my cuben tarp, to keep everything as minimal as possible.
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy