What Ron doesn't address is the question what economic parameters are collectively perceived as definitional?
I had a discussion about that topic here at BCT some weeks ago (I don't remember the thread title). In my opinion, there are not really "definitional" parameters, but there are a number of parameters that are foreseeable very difficult to change. These are those that strongly affect the "value theory" of Bitcoin (e.g. those limiting the coin supply) _and_ require a hard fork to be changed.
In hard forks there will always be a period with two different chains (if the network is not so small that at every code update 100% of all clients upgrade at the same time). So if you change a parameter that affects the "value theory" like the "21 million coins limit" in Bitcoin, then it's foreseeable that those that not change to the (e.g.) 21.000.001 version will promote their own version as "the original Bitcoin". They have a strong argument in favour and against a hard fork because Bitcoin's "value" is tied to the supply mechanism, and even if it only increases one satoshi in the hard fork, it's modified and will be considered "broken" by many. So the new chain with 21.000.001 coins perhaps can survive but from many will be considered an "alt coin". This is, like you say, a case of group psychology, but based on economic arguments.
A change of the PoW algorithm would, in my opinion, not affect the "value theory" directly, because we consider the current algorithm "secure enough", and so a change to another "secure enough" algorithm would not influence the value theory. Here it would be much less difficult - although not easy at all - to influence the users to massively update to the hard-forked version if it is advantageous to do so.
Where next for Slimcoin? I can discern a broad trajectory - the next phase will be a period of consolidation during which the added functionality is polished into something accessible and immediately usable. This involves creating more accessible descriptions of Slimcoin, descriptions which barely mention cryptocurrency at all.
... unless it is the case that collectively the group feels that Slimcoin should remain purely a store of value cryptocurrency - and we won't find out until the silent majority has not spoken (if you get my drift).
I agree here, although I find it hard to replace "cryptocurrency" if we must explain something that complicated like "proof of burn". But regarding more "accessible" features (like the "core payment function" or Web2Web pages), it may be easier ...