I've never coated such big sheets, but I'm a mural painter also .
Flat big brush and foam roller both will work. With brush you just have to work fast, to have last stroke wet when applying next one. This will make even coat. You can apply several coats, maybe 3 will be OK. Dipping in half-pipe tray with some cylinder weight inside will work (my friend used such thing to seize 100x70 cm sheets), but it will take more solution to cover paper on both sides.
If you're not in hurry, you can build coating apparatus (with half-pipe tray and overflooded liquid inside), one of this when paper only touches the surface of the liquid, and the surplus liquid is reused. If you need a sketch, I can make it. Feel free to post me to: luke.jastrzebski at gmail. com.