All the amps (Bose and Base) have connectors (C1, C2 and C3) on the bottom, but they're different among the two. You'll have a bear of a time locating them from vendors (get them cut off the donor car if you can) and they usually have minimum purchase requirements. Theres nothing like spending $100 for way more than the two $0.50 connectors that you need.
See the Phase II install on CadillacFAQ.com for pictures of the Bose amp unmounted. You'll have to pull terminals from the base amp (C3) and repin them to the Bose C2 pinout (reusing the same connector). You'll need two new connectors and terminals to pin out C1 and C3 on the Bose, as they're different from the Base amp. You'll likely need a small tool to depress the tiny clip on each terminal, and they slide right out. On other projects, a straighted paperclip works. Mind you, I've never done the Base to Bose swap . . . I've only studied the schematics and connector part numbers and pinouts (also on the FAQ).
As far as the air vent above the radio, just make sure you use a thin putty knife (2" wide), and NOT a screwdriver. You'll have to work it so the entire 2" width is between the vent and the dash on one side (try the passenger side first). Once it's in about a quarter inch, gently pry the side up. It will 'pop' when the clips release. Then work your way to the top and left side. Fold it up (there is a wire harness attached the the hazard button) and lay it on top of the dash.
After you remove the center screw in the middle of the ash tray, you pry out the ashtray/Heater control unit in the same manner. This will expose two bolts on top and two on the bottom of the radio head unit. Once you unscrew those, the radio slides straight out (no prying needed). Disconnect the connectors from the back before you remove it all the way.