Mappings cannot be referenced within the pseudo-constructor.
That is the ONLY solution I have come to. They simply. do. not. work. in the pseudo-constructor.
The moment I moved my line <cfset test = nameOfMapping.path.to.CFC() /> into the onApplicationStart() and out of the pseudo-constructor, BOOM, it found the file.
I may not know WHY it functions in this way, as the moment CF processes a mapping, I feel it should be readily available to be used from that point afterwards, but this simply isn't the case. I have spent hours on this problem trying every path combination possible, and only did I put my first attempt's syntax into the first BIF to fire off (onApplicationStart()), did CF finally respect the creation of the mapping and allow me to use it with the 'new' operator.
@Carl
This may have been why you chose to ultimately go with hard-coding those this-scoped variables for simplicity sake. I can easily see why. I think what I'll do before I try that is just use the non-mapped FQDN path for the first-run instantiation.