I ride with the IAM and am training to be an observer.
This issue causes more confusion than anything else that I have come across. I have spoken in some detail with many of the senior observers at our group and they all sing from the same sheet. I understand that part of the confusion comes about from a change in current thinking/recommendation regarding the second half of the "shuffle"
All thinks being normal and without the challenge of reaching the floor from a tall/loaded/heavy bike, possibly with short legs or an uneven surface this is what we suggest.
The final part of your stopping procedure should be done with the rear brake, (below around 15mph). In the (admittedly rare) event of very slippery road a rear wheel skid is more controllable. Additionally you have your throttle hand free for a rapid change of plan should your mirror check show someone behind you isn't stopping! You also maximise traction for steering instead of sharing front wheel traction between steering and braking.
If stopping for a short spell hold it on the rear brake with the other foot down. (I have deliberately not said which foot as it depends on whether you are riding a modern bike or a classic Brit machine). This maintains the brake light illumination and leaves you in gear and immediately able to move off when safe to do so or if someone appears behind you and isn't stopping.
For a longer stop, if it is safe to do so swap feet and put it into neutral.
Hold the bike now on the front brake with your foot ready to select first at a moments notice. You are able to get away in an emergency almost instantly assuming that you have stopped far enough from any vehicle in front of you and considered possible escape routes. (You may wish to reconsider this if you are on an older machine that does not have a front brake light switch and this in fact could be the reason behind a simpler shuffle these days).
When you have a warning that lights are changing imminently or there is an available gap in the traffic select first and swap feet so that you are again holding the bike on the rear brake.
When you move off you have one function for each limb to perform which seems simplest and most likely to result in complete control; gear lever foot supporting machine, foot brake foot covering the brake, right hand on throttle (and not having to cover the front brake as well) left hand on clutch.
To my mind this system gives the most complete control under "normal circumstances" but it isn't cast in stone!
And by the way, if riding the IAM way is taking all of the fun out of your biking you either haven't understood what you are being taught, you are riding with the wrong group or your requirements for fun require dangerous riding, most frequently riding too fast to stop in the distance that you can see ahead of you. Virtually every associate that rides with our group enjoys their ride and frequently have big silly grins on their faces when it all starts to come together and they find themselves riding more smoothly, more safely and actually faster.