Running Wall-Rated HDMI Cable Horizontally

I’m trying to run Wall-Rated HDMI Cable both vertically and horizontally behind the drywall. Have tried using fish tape to assist but have made zero progress because of the insulation and metal studs…anyone have success doing this? (See picture: going from a hole behind the TV to the cutout on the bottom-left). I’m able to reach the hole directly below the TV just fine.