Good Job, you are half way there. Obviously something is getting grounded. Something miswired? I don't think it could be too small of a fuse, Could it? Disconnect battery, Connect continuity meter to one side of fuse holder at a time, to good bare ground ,and see if you get continuity. (fuse removed, 4 way on). You should not get continuity. Exactly what fuse did you blow? Also, don't you have two flashers, one for turn and one for hazard? Both may need replaced to non LED. As Tim has indicated, there may be compatibility problems here. Your column switch should not care if it is switching incandescent or LED, so hook up the rest like normal incandescent.

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn