I decided to replace the heater matrix. As it turns out, it was a bit time consuming, but not too difficult. The Haynes manual is a good guide.
Here are a few random notes that might be of use to anyone else doing the job:
The heater box does not need to be removed, however, it does need to have to be lowered and rotated slightly to allow the matrix to be removed, so you do need to remove the 4 bolts holding the blower in place to do that.
The coolant needs to be drained, and the heater should be in the full "hot" position when doing that. There will still be some coolant in the matrix even after the coolant is drained, so protect the carpet with some plastic in the cabin, and some old rags or towels on top of the plastic in case any spills while you're removing the matrix from the car.
I did not attempt to remove the heater hoses where they attach to the matrix while the matrix was in the car. I disconnected the heater hoses under the bonnet and removed the matrix with the hoses attached to it. When installing the new matrix, I first attached the hoses, aligned the clamps properly and cleaned and refitted the insulation. Then I installed the matrix in the car and threaded the hoses back through the firewall.
Also, it was much easier to work in the car with the passenger seat removed. The lower console did not have to come out of the car, but I did remove the upper console, radio, and the air pipe going to the far left passenger vent.
There is a small connecting pipe which connects to the lower heater hose. The original pipe was metal. VW Heritage has a replacement (probably a VW classic part), which is plastic so it will not corrode. The part number is 171-121-140D.
The heater matrix is NLA from VW dealers, but the original part was a Valeo part and you can still find the Valeo part. The VW part number is 171-819-031E and the Valeo number is 812034. Meyle offers a slightly cheaper replacement part that is made in China, but I figured the original part held up pretty well. I replaced the heater hoses, which are still available from my local VW dealer and were not terribly expensive (171-820-371B). I also replaced the expansion tank as it was difficult to see through it had yellowed so much. Also available from the dealer (171-121-407F).
There has been some discussion about coolants. The original fill in this car was G11. The only coolant VW carries now is G13. Some people say G13 isn't good for older cars. When I bought my car, it was serviced at my local VW dealer who replaced the radiator and water pump and flushed the cooling system and put G13 in. While I don't think there is anything wrong with the older coolant, I didn't feel like converting back, so I am continuing to use G13 in the car. I did email Volkswagen UK with the question and their response was that G13 is compatible with older VWs like this. I think it's probably more important to periodically change the coolant than to worry about whether you're using G11 or G13.
A few pictures:
Lower shelf removed and heater matrix door removed. There was no evidence of leaking when I just opened the door and took a look, but whenever I would turn the heater on, there was a slight smell.
Original matrix removed - now you can see what I was starting to smell something. (Note - the coolant on the towel came from the disconnected heater hoses, the matrix leak was very slight).
Valeo replacement - identical except for the VW/Audi logo:
Things taken apart:
Heater matrix slot in the heater box:
Old vs new connecting pipe:
Original and new VW expansion tanks. Big color difference. The tank was not originally this yellow/amber - it was actually white, or pretty close to white.