ah yes, but your worry (or was it purely jest?) expressed in your post highlights a good example of the faulty thinking that ensures we continue suffering the pain, shame and life restriction of shy bowel.

...lets look at the sound princess situation a bit more:
as sufferers of shy bowel, we think that other people are
a) gonna hear that we flush twice and register it as important in their mind, and
b) judge that we have done a dinosaur sized doo doo in the pan.
and
c) draw some negative conclusion about what this means about us as people.
and
d) perhaps even make a negative comment about us and laugh at us.

but if we examine this scenario and our thought processes, do we find that it's realistic?
firstly, if you use the sound princess while you're poohing, there's gonna be a gap of silence while you're wiping your bum (or in the case of men especially, just sitting there enjoying that post-poohing bliss!), and then you're gonna flush the toilet. so, if someone WAS listening out and registering the number of times you flushed, they might easily come to the conclusion that when you went into the toilet, it wasn't as clean as you wanted it, so you flushed BEFORE you poohed (the first flush), and then obviously, flushed after you poohed.

however, chances are that the other people in the toilet won't be bothered about how many times you flush, just because they're more interested in their own lives. and that's an important point: as people with a form of specific social phobia, we are under the unfortunate delusion that everybody else is really very interested in our lives and especially our toileting habits... when the truth is more like: other people don't give a shit about you by-and-large; they're much more interested in themselves, and how well or how badly their lives are going. all people are essentially ego-centric.

but for the sake of argument, let's say you're in the toilet at work, and other people are in there. (and i get that women are more likely to hang out and chat and spend time putting on their lippy in toilets than men are.) well, you've still got various healthy options available:
either you can just say to yourself, this is not gonna work for me, there are too many people taking way too long and hanging around outside my cubicle, and they're chatting and i don't particularly like them anyway etc, in which case you just walk away from the situation and come back a bit later when you get an urge again and see if the toilet is more empty second time round.

or else you can rationalize the situation: you're on the shitter: you've got a good ten minutes in there without anyone batting an eyelid, so take your time, text your friend, do breathing exercises, read the paper, or do a crossword or sudoku. eventually the other people will leave. see if you can go, maybe using the sound princess if you'd bought it, and if you can't (don't strain excessively, it'll just give you piles), then again walk away from the situation. at the very least you're starting to turn your behaviour around.

or thirdly, you could just go for the f*ck 'em option. cultivate an attitude of "f*ck 'em!" generally in your life (very beneficial for people with social phobias of any kind). you're in the toilet, you went there to pooh, and to hell with anybody else and what they think or don't think about you. and if you manage to go, you go, and if you don't, you don't, no big deal, but again you're starting to turn your thinking and your behaviour around, and that, over a period of time is powerful.

the bottom line is poohing (no pun intended!); you wanna go somewhere and be able to pooh: that's your goal. so be gentle with yourself and set up the situation in any way that helps you.