I'm about to blow everyone's fucking mind.
The 48hr cool down on leves is somewhat a myth/wrong!
I went to Limsa, Ul'dah, and Grindia today. Today having been 2 days since new leves happened. So I wanted to do all battle leves for my 8. Only way to do that is to travel to all the nations and get their level 10 ones for battle leves. So I did 3 at Limsa, 3 at Ul'dah, 2 at Gridnia. Came back to Limsa, checked counter and it let me trade them back in for new ones already. Had been maybe 5 hours?
So I tested it. Grabbed 3 at Limsa, did them. Went to Ul'dah for 3, did them. Now I'm in Gridnia and did 2 more. Game crashed on me and I was going to back to Limsa to see if I could cycle them once again, but I'm pretty damn convinced you can.
All you have to do is travel folks.