While the question asks "How to Level Magic Skills as a Warrior" the reason why you ask this, as stated in the question body, is because you want to get to Level 80.
It seems to me that to get to level 80 I will need to level all my skills to 100. Easier said than done though.
As a non-magic-using warrior, how can I level my various magic skills? Let's ignore Restoration, I actually use that from time to time. But how can I level up the other skill trees?
you can do this and more without even touching magic skills since the 1.9 Patch which allows your skills to become Legendary
The purpose of making a skill Legendary is to allow it to contribute to increasing character level again. In Skyrim, character levels are gained by leveling up one's Skills. When all skills reach 100, the character can no longer gain character levels (this occurs at level 81). Making skills Legendary allows skill leveling to continue, which in turn allows character level to continue to rise.
this means you just need to make your Warrior-centric skills Legendary and just keep working on them, as such to reach Level 80 you don't need to level up every skill to 100, just the ones your going to use far more often
otherwise if you are looking to make your Warrior a magic user regardless, the answers here (provided by Studoku's comment), particular the accepted answer is a good reference