Sorry for the delay. I have been doing Dex-Cool to John Deere Cool-Gard conversions for a few GM vehicles.
I use these directions when doing coolant changes.
Coolant Change Guide For Neglected & Converted Cooling Systems
Coolant Change Guide For Clean Cooling Systems
G-05 will work perfectly fine in any cooling system that used the old green stuff. I personally like John Deere Cool-Gard which is a G-05 formulation. It even has SCA in it for diesel engines. It is safe for gasoline engines. John Deere recommends Cool-Gard for all its equipment going back decades ago. It's good stuff!
City water usually contains haloacetic acids, trihalomethanes, chlorine, barium, chromium, fluoride, nitrate, selenium, and sodium. Well water has even more crap in it. This is why deposits and scale form in cooling systems. USE DISTILLED WATER!!!
Following the directions above for neglected cooling systems, you could just let the Firebird idle on the blocks if it is safe to do so. If not, wait until you can drive it.
The places that do coolant changes usually use a coolant exchange machine which gets most of the old coolant out then replaces it with new coolant. These machines can only get about 80-85% of the old coolant out of the cooling system. They typically don't clean out the cooling system. They just replace old coolant with new coolant. Using the directions above will get damn near all of the old coolant out and clean the cooling system. A lot of folks whot had GM vehicles that had shops/dealerships convert them from Dex-Cool to the old green stuff had machines such as these do it. With 15-20% of the old Dex-Cool still in the cooling system, it is easy to see why there was still red crap showing up in the cooling system. I also seriously doubt these places use distilled water.
Regular green is disappearing from store shelves. Eventually it will be gone. Why stock a coolant that only lasts 3 years/36,000 miles and has a rather low shelf life when there are replacements such as G-05 that lasts 5 years/100,000 miles and have longer shelf lives? It's all about shelf space.