Hi Tom
Somebody beat me to it and posted the AFM for the G550.
I always question why we do things as well as you seem to do. So many things we do are left over from long ago with entirely different machinery.
If everything is normal I retract the gear and then do flaps at 400' as long as I have reached the required speed by then. If I am heavy and its hot I might not be there by 400'. (Our FD goes to a pitch that gives you V2 on one engine). Once flaps are raised the speed schedule changes and we can select a vertical mode. (FLCH, vnav or VS). I hate FLCH, so I usually go VS and enjoy hand flying the plane while monitoring speed.
If everything goes to hell we hold v2+ to 1500' or msa. Then level off and accelerate.
By leaving the flaps to 400' I am covered in case one quits. Other than that I like it and it works. Since I am the PIC I do it my way.
The other more interesting thing I have always argued is that if you need the performance why not start the takeoff with flaps 20 to get the shorter roll, then if an engine quits bring the flaps to ten and get rid of the drag. I have not gotten any traction with that at all.
Good luck with your arguments, you make some good points. Always ask "why".