The stage terms are somewhat outdated, and there probably isn't a single definition for the work beyond 1.
The old HD SE catalogs used to specifically list the parts and kits as "stage 1," "stage 2," etc. There are still some reference to it, but its a bit cloudier now.
So- here is my interpretation/memory:
Stage 1: pipes, air cleaner, and fuel managment
Stage 2: hot cams
Stage 3: header work (for example, the Sportster conversion kit to go from 883 to 1200 is the Stage 3 kit because it changes the headers)
Stage 4: all the other madness. The stage 4 kit in the HD catalog includes heads, throttle body, cams, pistons, pushrods, and clutch.
And- going with a turbo would be the equivalent of getting the stage 4 done.
I did the stage 4 bit at time of purchase so everything was part of the original warranty. Including labor, are you still under $6500 for the turbo? I've never ridden anything like that- and Im sure my stage 4 does not compare HP/T wise to what you're looking at.