Have you tried to backflush the core yet? My old 93 would need to be backflushed every year as we got to winter. The Dexcool crap will buildup in the pipes with all the 90 degree bends and eventually slow the flow through the heater core. I used to drain the radiator, disconnect the hoses at the water pump and engine and hook the garden hose up to blow the crap out. You could see all the buildup come back out and I'd be good for a year. The 93's had the worst heater hose routing of all the 4th gens though. The fact that you have a wet carpet is not a good sign though. It still might be worth the backflush first.
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69 Z28 JL8 4 wheel disc brakes - being restored
09 Silverado Z71
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