I ran around with a bypassed heater for many years until a few months ago. Luckily Robsport persuaded me to buy the seals a couple of years ago before they went NLA as they reckoned a leaky matrix was unlikely.
I fixed it last summer. Robsport were right. The seals had hardened after 12 years of use (back in 1992) but had let go due to the rusted mild steel heater pipes inside them breaking out the seal. By the way, replacing them is not a simple job. Pipes out = Heater out = Dashboard out.
If your original pipes are like mine, they'll be unuseable as nothing will seal against a rusty surface. I bought the Stainless Steel replacements from Robsport which fitted quite well, but will be totally useless without the rubber seals. A pair went for £20+ on ebay last year in the UK.
I believe other BL creations, SD1 and possibly Jaguar, also used the same heater system so other classics should be in the same boat.
The heater matrix appears to be made from some sort of softish alloy, brazing or soldering will only accept a limited amount of vibration so an extension stub sounds like a good experiment. An old school plumber with plenty of solder might be helpful. I'd offer you a scrap matrix to practice on but the carriage is a bit steep to the other side of the world...............
Adam
TR7 V8 DHC Jaguar Solent Blue. 9.35cr Range Rover V8, Holley 390cfm, JWR Dual Port, 214 Cam, Lumention, Tubular Manifolds, S/S Single Pipe Exh, 3.08 Rear, 200lb Spax & PolyBushes all round, Anti- Dive, Strut-Top Roller Bearings, Capri Vented Discs & Calipers, Braided Hoses, 4 Speed Rear Cylinders, Uprated Master Cylinder & Servo, AT 5 Spokes and Cruise Lights, S/S Heater Pipes, Replacement Fuel Tank. No Door Stickers. Mine since July 1986, V8 from 1991