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I have to advise right out of the gate that this is a MUCH more involved job than glove box removal. After raising the vehicle and removing the heater and a/c lines (as well as recovering a/c refrigerant) the entire dash must be removed from the vehicle. After dash removal the hvac case must be removed and disassembled. Basically you would need to disassemble the dash down to the firewall. It is quite an involved job and takes many hours to complete.
If you found a shortcut that is great, I can tell you however that GM service information clearly states to remove the entire hvac case.
Heater Core Replacement Removal Procedure
Air Conditioning and Heater Module Assembly Removal and Installation
J 39400-A Halogen Leak Detector
Notice: Refer to Fastener Notice in the Preface section.
Tighten Tighten the bracket nut to 10 N·m (88 lb in).
Tighten Tighten the heater case plates nuts to 10 N·m (88 lb in).
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