I finally found a few minutes at work today to disassemble and assess my situation with the heated barrel.  It came to this because my Cupcake just wasn't extruding well anymore.  Here is what clued me in -- ABS leaking from between the nut and insulator.

I started off by carefully removing the kapton tape wrap, which was a complete PITA.  First, off with the thermistor:

Now, the kapton was really getting to me, so I carefully used an Xacto knife to cut down the side, then peeled away the wrapping:

Here's what the nichrome looks like now.  I think it had a tan-colored insulation before, but now it's white.

I then stuck the PTFE end into a vise and removed the nozzle.  The hardened ABS was actually pretty interesting.  There was a hole down the middle, which made me think that perhaps this was making the extruder work too hard?  Or maybe this happened after backing out the filament, and the residual ABS formed a shell inside of the barrel?

Now I wanted to get the barrel out of the PTFE insulator.  I cranked down on the insulator a bit more in the vice, then threaded a second M6 nut on top of the washer and tightened it.  Then I unscrewed the barrel by using a wrench on the bottom M6 nut.

Check this out -- I had some ABS on the end of the barrel, so most likely the barrel did get unscrewed from the PTFE and ABS collected in the gap -- exactly what people have described as causing extrusion problems.

Tomorrow, maybe I'll find time to reassemble this.  Everything looks like it's in good shape, so I don't think I'll need to replace any of the parts.