I stuggled a bit with my deep water starts and someone gave me a tip the other day that really helped.
Keep really balled up as the boat pulls you and keep your weight back, your arms shouldn't be doing anything apart from holding on, so don't try and pull yourself up. If the board is sinking and you are facing planting chances are you are not keeping your knees up against your chest for long enough and your weight back.
Keep your arms around the outside of your knees and if it helps put your hands close together on the handle, this brings your arms across the front of your knees and and use your foearms to help you ball up.
Worked for me...