Running a solid or flexi type of fuel hose in the heater channel wouldn't be a great idea for two reasons, the first which would drive most people mad is the noise, every time you hit a bump it will rattle about especialy if it's the solid type, the second only realy applies to the solid type, if it does rattle around it runs the risk of fracturing, then you'll have a heater channel full of gas/petrol !!!!!!!
I would use stainless fixings (screws or rivets) on this type of clip

I know you don't want to drill in to your chassis, but considering the time you have spent on it the last thing you want is for it to catch fire
Rob.