RE: Routine for home training around compounds
Synaptic facilitation chins really helped with my chinning. It would suit you as you have a home gym... Drop chins from your routine and, instead, do chins throughout the day, maybe 6-8 singles. Just keep doing it and you'll soon see an improvement in your chinning. Make sure you use full ROM. Heavy bent rowing should also help. Also, look at your bench technique to see how its affecting your shoulders and do some RC work.