They called today and told me that it was going
>to take longer than expected because (and here is my concern) they need to
>take out the seats and pull back the carpeting to get to where the steam is
>coming in.

I would wonder if they are trying to charge you for unnecessary work or
just don't have a clue.
Someone correct me if I'm wrong here. It's been a couple of years since we
replaced our rear heater core.
(I'm looking at pg 80.16 of Bentley, Additional heater, under rear bench
seat [All Water Cooled])
The steam could really be from a couple of places realistically.
Either:
the heater core itself
OR
A hose leading up to the core
The core itself should be accessible by removing the cover, disconeccting
the hoses, take out the heater box and then remove the core from within.
The hoses are a fairly short run between the grommets at the sheet metal to
the core. My hunch is that there is a leak possibly spraying on the fan.
That could explain the volume of steam in such a short time. It's hard to
tell if the fan is interior or exterior from the diagram and it's been a
long time since I looked directly at it. Might do that tomorrow :-)
I'd see if they have really looked at the hoses as culprit before pulling
out all that at your cost.
Have they pressure tested the system and bent some of those hoses around to
see if there is a small leak? I bet there is.
 If you have old (original) hoses you may want to just go ahead and replace
them all now. Its a lot easier than doing it beside the road-at night-in
the rain-during a snowstorm, etc.
Let us know,

Dave C.
Williamsburg, VA
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'85 GL Westy (His)
'91 Cabriolet (Hers)