I've been working on a similar project, but easier because I'm not trying to transfer heat from a solid - that's pretty hard. I'd be careful about flattening the copper tubing - the metal thins out and you don't know if you'll get leaks a month or a year from now.
Take a look at CPVC tubing - it handles high-temperature situations really well and doesn't crush easily.
Take a look at CPVC tubing - it handles high-temperature situations really well and doesn't crush easily.