I am what many here would call a "Calvinist", as what I believe on each of the so-called "Five Points" matches them... at least in spirit, if not in letter.
My only misgiving in the OP is in the conclusion below:
There are actually those among professing Christians ( like myself ) who see the things that are termed "Calvinism" all by themselves in their own studies of His word... and have never relied upon the doctrines established by John Calvin and his successors to guide them or even to influence them in any way whatsoever.
Most, if not all, of us come from backgrounds that are "non-Calvinist" / "Arminian"/ "etc." in their origins;
With me personally hearing God's word and believing on Christ for the forgiveness of my sins in an independent Baptist Church that taught what many are now calling, "Provisionism".
While the teachings of "Calvinism" may, in most cases, mirror my own beliefs... they do not do so in their entirety.
But on the so-called "Five Points", they do indeed.
Regarding salvation, faith and the natural condition of man:
I do not agree with the teachings of Jakob Hermanszoon ( "Jacobus Arminius" ), whose followers presented their Five Articles of the Remonstrants to the churches of the Netherlands in response to the Belgic Confession;
I also do not agree with the teachings of John Wesley, who went on to found what would later be known as "Wesleyanism" and the Methodist Church, and those teachings are generally known today as modern "Arminianism";
Finally, I do not agree with the teachings of the Roman Catholic Church, whose views on salvation, etc. were codified by Luis de Molina and is generally known as "Molinism".