Decades ago, the '64 GTO was roundly criticized for getting very marginal brakes, same drums/shoes as a base 6 cyl Tempest. I have a '64 so know it best. I believe PMD made some improvements but don't think the rear brakes had improved much by '69. The availability of front discs was a big step forward but the rears were still marginal.
I can recall various recommendations for improving the brakes. IIRC, one of the recommendations was to install aluminum rear drums which could be found I believe on big Buick station wagons of the era. I believe these shoes/drums were significantly larger than stock.
I don't recall whether these drums could be installed directly or required swapping the backing plates.
I mention this because perhaps your fit issue is a result of a PO swapping on big car rear drums.
Have you ever replaced the shoes? If not, you might compare the GTO shoes you have on the car with the ones the parts store would sell you as correct for a '69 GTO. You might discover you have bigger than stock rear shoes/drums.
Just a thought.
Checking the p/n on the backing plates should also help determine what you actually have on your car,
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