Cloth strap wrench will not damage the pulley one bit, this should of been an easy fan removal.
If you had a cast iron idler pulley most LR's had a snap ring (older D1's) allowing a $6.45 quality brand sealed bearing replacement, not some POS bearing from China. Even the cast iron idler when the bearing gives out begins spitting out balls cocking the idler then your screwed. At least the steel idler will not melt or fall apart only requiring snap ring pliers, spare bearing, a couple wrenches plus one long handled wrench special to backwind the tensioner spring allowing reinstalling the belt. Always a good idea to carry a new spare belt also as they can get shredded when been popped off. Count your blessings the belt and fan didn't lock up bending blades then ripping a circle out of the $$$$$ radiator.
Repair time not counting the 93 minute road trip rescue with idler removal, replaced bearing, reinstall idler and belt to turn key running again, 22 minutes. Cost of rescued friend's LR one Bier a minute repair bill plus a lunch......~~=o&o>......