From reading your post I don't think you've made any mistakes, it sounds like Jack is doing pretty well. I've done a list of commands I use for my lot and what they're for if you want to compare. Rodaidh responds to varying strengths of the stop whistle and different hand signals for different commands,
long hard blast on stop whistle - stop, lie down and look at me
shorter soft blast on stop whistle - stop, stay standing and look at me
arm out palm outwards - stop, stay standing and look at me
arm out palm down and downwards movement - stop, lie down and look at me
I use the harder whistle if he's made a flush and the guns are about to go off so he's down out of the way and I use the softer one if he's hunting for a bird or dummy and I want to stop him on his feet so I can signal him to look somewhere else as he will need this for competitions. Alfie and Tilly will stop to the whistle, verbal command and hand signal but they don't sit or lie down unless I tell them to, they stop but stay standing and this doesn't affect their working on shoots at all. I'm not really bothered what they do as long as they actually stop and pay attention to me, it's only Rodaidh who I really need to respond to more nuanced commands. That Jack sits to the whistle, verbal command and hand signal and at distance is really good and I don't think that him sitting to the stop whistle is going to be an issue on a shoot but if you want to train him to stop and look at you but not sit then do it, it certainly won't do him any harm to know it but I wouldn't say it's essential for him as a working dog. As for teaching him to lie down I would probably do this as well, again it's not absolutely essential but it's not a difficult one to teach and shouldn't take very long.
I use the following verbal commands with all 3 of them...
'sit' or 'down' - sit or lie down until I tell you to do something else, that could be 10 seconds or 10 minutes
'whoa!' - stop, stay standing and look at me
'look!' - to get their attention, usually used if they have their heads stuck in a bush or something and I just want them to look up
'wait' - used on walks if they're off lead they don't go any further until I catch up with them and also when getting out of the car so they don't just leap out as soon as I open the door
'stay' - don't use very often but they know what it means so use it sometimes to reinforce the 'sit' or 'down' in a very high distraction environment (usually for Alfie!)