what about "market anarchist"?
personally i think you are a bit too concerned about "offending" folks with a label, but maybe that is just my own reaction to the widespread effects of identity politicians (aka the language police). ;-) but i definitely appreciate your desire to engage in a meaningful way.
"They differ from the anarchistic individualists in their belief that men, if freed from coercion, will enter into voluntary associations of a communistic type, while the other wing believes that the free person will prefer a high degree of isolation."
any one-size-fits-all perspective like those is highly suspect, imo.
individualist anarchists that i know do not in any way support "private property", but rather think in terms of "personal property", which has to do with usage and possession rather than ownership. obviously, no state is required for folks to have and use resources, those folks just need to be ready and willing to deal with interactions with other folks that may involve those resources. for sure, sometimes shit will happen that ain't too cool with me. but i'd be quite happy to take my chances in that stateless world, building meaningful personal relationships to better deal with such unwanted scenarios, without the coercion of institutions.