Dale - a lot of us here call an action that has been re-barreled and settled into a new or new style stock, with new trigger and scope and all that a custom rifle. Some folks call a dressed up mil-surp a custom, or customized rifle.
No matter what you start with, unless you create the action and bolt yourself you are buying or using someone else's creation. How or what you barrel it with or what the caliber eventually becomes, it starts out with someone else's action - a Rem 700, Winchester M70, Savage, Springfield, Mauser, P14/M17, etc., etc., etc. Same thing with barrels - unless you cut your own, you purchase someone elses and the same for stocks.
So it really depends on what your definition is. If you feel your Rem 700 in a 260AIx2 with a gizmold stock, burpies trigger, eyeballess scope and slap happy mounts is a custom rifle, then that is exactly what it is for you. Someone else might disagree but he doesn't own your rifle and may not have anything like that himself.
Most of the items you considered not being custom is what many feel make a custom rifle. I think the concept of 'preference' might be the broad based definitive phrase here. JMTCW. Mikey.