Your references are very helpful. Have you read them carefully?
There is no point in simply putting the word 'exist' in bold, as though that answered the question. The point about a solipsistic position (and philosophy generally) is that it questions the meaning of words like 'exist', so just repeating them begs the question we are discussing.
Let's take your first quote: ...Solipsism is therefore more properly regarded as the doctrine that, in principle, "existence" means for me my existence and that of my mental states. So that is what a solipsist understands by 'exist'. Now consider your original point:
So the solipsist's understanding of any 'existence' of this forum would therefore be that it 'exists' as part of their own existence and their own mental state. So yes, it may be that a second solipsist shows up, but they too would be understood by the solipsist to be part of their own existence and their own mental state.As Searle (*) pointed out: solipsism refutes itself. If you're a solipsist, you don't believe this forum and its people actually exist. Expecting that a second solipsist shows up implies wanting solipsism to be proven false.
Seriously, I assume you do recognise that solipsism has a long history in philosophy. Do you think this is because philosophers had failed to notice there seem to be other people in the world? Or because they had no access to reference books that would have put them right?
The history of philosophy is packed with variations of this position, all versions of Idealism. Surely you have come across them before? You are welcome to disagree but I am puzzled why you react as if I am saying something wildly eccentric and original.
((*)I am also sorry for poor Searle who is being badly misrepresented)