Then I don't know how to convince you.  How could one establish the proof that entities X have no power of decision on outcome U ?  I would think that if one proves that if outcome U is largely independent of whatever X does, the proof is established, no ?

Of course, we cannot do real experiments, but Gedanken experiments are good enough if we take into account all logical possibilities, and eliminate only those that can be agreed upon to be highly improbable.  That's an accepted practice in many fields of study.

As such, I think I established that even in the extreme case where ALL non-mining nodes disagree with a miner protocol, that miner protocol can nevertheless be the actual one on the block chain.  You already agreed with me that this was true when all miners (like they are used to do) have a common protocol and didn't deviate from it.  In that case, there's only one block chain out there, and full nodes can accept it, or can stop.  But they cannot FORCE miners to accept THEIR version of the protocol.

You raised the case when miners were not united, but a fraction went with the full nodes' protocol preference.  I just demonstrated that if the miners disagreed, then we have a hard fork, and there are now TWO CHAINS out there.  So in general, some full nodes will download chain A, and others will download chain B.  The most extreme case, is where all full nodes refuse one of both (say, refuse A), and ONLY download B.  I demonstrated that even in that extreme case, under reasonable assumptions of behaviour of exchanges and users, the relative values of both chains, with the eventuality of one actually going to zero, is entirely determined by what the market will do in this case, and AGAIN, the full nodes refusing chain A can very well result in chain A being the dominant one, if ever the market decides so.  So in the case you raised, too, whatever the full nodes tried to impose, has no effect on the outcome.

If that is not a sufficient proof that whatever full nodes do, they have no *decision power over the protocol* I don't know what could convince you.

Now, I will agree with you that they have some "psychological power before the split".  It may be a vague indication of what users MIGHT do if ever they were given a choice in the market.  But even that is very limited: full nodes are not representative of the market. They do not faithfully represent the stake owners, and they do not faithfully represent the traders.  They, especially, do not represent newcomers to bitcoin that will also vote in the market.  So their indicative power of what the market might do, is not necessarily of much value either.  It is only in the case where miners are very hesitant to fork off, and are too incompetent/lazy... to do a serious market study, that they might take full node preferences for a market study to base their decision to fork or not, on.

In any case, bitcoin is constructed such, that "forking away" is risky for miners, because of the slow difficulty adjustment.  Miners need to know that they will fork off with big majority before attempting to do so.  So, if full nodes can influence anything, they may *increase the pressure on miners NOT to fork away*.  If ever full nodes in majority keep the old protocol, miners might take this as an indication that, if ever they fork away, the market will not support their initiative, and it will even be harder for them to fork away.
But at no point, full nodes could IMPOSE a CHANGE upon miners, if miners are not convinced that they will fork away with large majority of their peers, because in as much that full nodes are an indication of what the market would do (even though, as I said, this is highly doubtful because they are not representative), they STILL face the difficulty adjustment question.

edit: I would like to point out that I am not trying to do any politics here.  I simply see some claim that "to stop the Russians, we should all have plastic guns" and that a whole argument of how it is important to keep the number of plastic guns high, and how some measures cannot be taken because the number of plastic guns goes down.   Just by logic, my point is "plastic guns won't stop the Russians", and I try to argue all cases where plastic guns would be used to try to stop the Russians, and obviously fail if you think about it: if ever they are stopped, or not, it doesn't depend on holding plastic guns.
So I'm putting into question the argument that plastic guns are important, because it sounds obviously false to me.  That's all.  After I've listed several arguments, someone tells me "you've still not convinced me that plastic guns won't stop the Russians at all.  Of course, with ONLY plastic guns, we won't get there.  But I think they still play a role in stopping Russians".