First and foremost - I'm not a professional plumber - but do a lot of DIY projects.
Were it me... I'd forgo the copper tubing and use plastic. Much easier to run through all those twists and bends... (somewhere, you're going to end up splicing that copper, making leaks more of a distinct possibility. With plastic you'll have a better chance of a solid run. Also - even if florida it gets cold every blue moon... bury the tubing in the insulation as close to the warmth as possible.
Otherwise - I'd go for it...
Assuming there is no other water access closer to the end product.