We seem to be stuck on the word 'existence'.
As I understand it you are saying that things always exist and that names are superimposed on those existing things and that we are independent of those things.
My point is that things are a product of mind and that naming asserts their identity (id-entity). Prior to naming there are no things, and non-existent 'things' cannot have separate existence (whether they be you, I or the tree). This is how I use the word 'existence'. In Buddhist parlance prior to assertion = the unconditioned, post assertion = the conditioned.
In order to demonstrate my point you are invited to look around you without creating names (thinking or asserting) and allow the senses (seeing, hearing etc) to function unimpeded by definition... Where are the 'things'?
Prior to assertion (naming) the eyes see but no names are attributed for the defining process has yet to act and define the objects with which we interact.
Just a view - nothing more...