There will be no interference with carbs and gh timing. You can take your GH regardless of carbs and it will still work but if you are trying to get leaner and doing fasted cadio, I would take a dose before AM fasted cardio. I would split your dose up through the day, taking no more than 4iu at a time. If you are going to pick one of your doses to be slightly larger, I would take the larger dose preworkout. So with the dosing you have now, I might do 3iu in the AM, 3iu preworkout, then 2iu before bed. When you go to 12iu, I would take 3 doses of 3iu per dose. I take my doses IM through the day and then Sub Q before bed
Just as a general note, with your intra workout shake, I would lean toward EAA or pepto pro instead of BCAA and if you are going to use carbs, I would use a waxy maze or HBCD