Did the original radio use a support on the back of it, or was it held in place by the nuts on the control knobs. If it did use a support (which I feel it did) where did it connect under the dash.
Don't know for C bodies as it's been about 30 years since I pulled a AM 8 track out of a 68 Polara but b bodies have a arm with a slot attached to the dash back there. There's threaded bolt on the back of the radio which slides into the slot and you screw the nut down on the threaded bolt coming out of the back or back side of the radio. In the front behind the faceplate there's a couple holes in the dash frame. You screw two small radio bolts into the face of the radio body. Install faceplate and done.
i see your dash is of the knob variety so probably the correct radio is held in by a nut on the the knob post with the nut on the outside of the dash.
The back probably has a threaded post coming out the back or back side area.
good luck
A/C ducts will probably be in the way but hopefully not or you can contort to get around them or take them off temporarily.
update:
here's some crappy photo's of a B body thumbwheel which is probably very similar to yours except i seem to recall C body radios came to a point in the front vs being flat across the face other wise are extremely similar. Also some of another style radio knob style as opposed to thumb dial
First one is 68/69 B body style thumb wheel AM/FM front note red circle on the left ... there one on the right too out of the pic those bolts go through the dash and into the radio in this style
I'm not positive but I think this is the back of that top radio note the bolt sticking out side toward back .. some are on the back some on the back side
this is the 71 and up B and I think maybe 70 and up C body style ?? not sure exactly what but has knobs instead of thumb wheel see the bolt coming out the back
front of 71 and up B ?? and I think maybe 70 and up C body style ?? .. control knob studs to through dash frame and nuts tighten up and hold it fast
I did this real quick and dirty so If i made any errors or omissions I'm certain someone will come and along and point out if I missed or misstated something. Especially what the knob style radios actually are
Good luck mopar brother
