If all of the wheels seem to be locking, I'd put my money on a dud master cylinder. If the car seems to be pulling to one side, see which wheel hub feels the hottest after a drive and that will usually be the suspect corner.
As these cars don't have boosters, split systems, proportioning valves and disc calipers the system is much simpler to diagnose and fix.
In the first instance, I'd just change the brake fluid and see if that makes any difference. Brake fluid absorbs water over time, which when heated expands and can lock up the brakes, or conversely, when it vapourises to steam, the pedal then goes very soft because steam is a compressible gas. Checking the flexible hoses and movement of the brake shoes while you are bleeding the system with the wheels and drums off, is also always a good move. This is simple routine maintenance and will give you a lot of information on the overall health of the system.
If the problem persists, remove, strip and rebuild the master cylinder. Kits are available.
If you've done all of this and you still have a problem, buy another car ...
My humble opinion,
Chris