im badges are WAY easier than shards. ive only amassed about 500 in my whole time @ 80. i bought the boa trinket, and the lvl 80 shoulder enchants (too lazy for hodir)
2 badges for h daily, 4-5 from the instance alone, then you have all the other heroics, AND raids....hell you could prolly get 120 badges in a week.
the shards you obviously need WG for and then need to grind. it would be best if you had 4 friends who could help you out. go win wg then start a quick heroic zerg to maximize shards per wg. also do the wg weeklies.
GL with your project!