The decision
You've got the argument and the method. What's left is to decide, and I'd like the decision to fit in one sentence.
Before I say yes, I ask the price, and I only pay it if I'd have chosen it on my own.
Three parts.
The first is the question, before the yes, to the organiser or the menu, for the all-in figure, said to yourself as a number.
The second is the test. Would I have chosen this if nobody were watching? Hold the number against the wanted column. Yes is allowed. It just has to be yours.
The third is the sentence. The counter-offer once, then the quiet no if needed, warmly, with no speech.
There's a form of planning that helps with rules like this, and it's been tested many times. Peter Gollwitzer and Paschal Sheeran reviewed ninety-four studies of it in 2006. You decide in advance what you'll do and when, in the form "when this happens, I'll do that", and people who plan that way follow through much more often than people who only hold the intention. So write three.
When a plan arrives in the chat, I'll ask the organiser roughly what it'll come to before I reply.
When the bill comes and someone says "shall we split it?", I'll say "I'll just put in for mine" while getting my card out.
When the price is more than I'd have chosen, I'll offer the cheaper version once and then say "I'll skip this one" if it isn't taken.
What to expect. This is my expectation and not a finding. The first time you ask the price it'll feel like a small transgression, and the organiser will answer within a minute and nothing will happen. The first counter-offer will be taken or not, and either way someone will message you afterwards to say they'd been thinking the same. The first "I'll put in for mine" will be followed by someone else doing it, and the split will be quietly retired at that table within three dinners. By a month the question will be automatic and the feeling of rudeness will have gone. The month's total will drop, and the first month you see it drop is the month the wanted column starts to look possible. You'll still say yes to things. Most of them will be things you'd have chosen, and those evenings will be better, because you won't be watching the bill.