I have a theory...
The backing plates are 68 and older B,C body 10x2.5?
The hardware and the backing plates match pre 69 parts
The rear seems to be a 76 7 1/4 with 1/2 inch studs, 5x4.5 bolt pattern and the large center register.
Dr Frankenstein would be proud
Evidence...
Car is a 76 /6 which got 7 1/4 but with BBP
Mechanic states the old shoes are 10x1.75 simple measurement. A lot of difference between 1.75 and 2.5 I doubt he mis-measured
67-68 10x1.75 backing plate
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OPs backing plate
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69 - 76 Automatic adjuster cable
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OPs automatic adjuster cable (pre 69)
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10x1.75 69 up backing plate, the spacing is tiny
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OPs backing plate, the spacing is huge compared to 1.75, easily 3/4 of an inch more
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So my theory...
The backing plates MIGHT be correct for 10x2.5 brakes only a test fit or some measurements will know for sure.
The backing plates and hardware came off a 68 and older rear
Somewhere along the way someone put 10x1.75 shoes on (how they fit is a mystery to me, The shoes being narrower would not interfere so in theory it could work)
I believe the OP needs to go to a local auto parts store and buy 10x2.5 rear drums for a 76 Dart /6 rather then ordering them. Taking the old drum that fits the hub and the studs and the backing plate along for size.
This can also be done to determine what drum the backing plate fit
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