Sure enough, that's the 1978 version. All the electrolytic caps in a 40-year old radio are on borrowed time, regardless of the radio's "mileage".
The symptom you're having is not one of those "they all do that" sort of commonly-seen problems.
It's possible that replacing all the electrolytics would fix this fault.
It's also possible that the receiver-overload fault is caused by some other failure. If so, you'll still have that problem after the radio is re-capped. No other way to find out, short of taking an oscilloscope to probe the receiver's AGC circuits to track down what's failing. That's probably what I would do first.
Reminds me of a 1978 car with one cylinder misfiring. Replacing all 8 fuel injectors, plugs, wires, cap and rotor would probably be a good idea. But if it's still missing on one cylinder after doing that, it's the only way you would know that it didn't fix the trouble.
If you decide to tackle the "re-capping" project I recommend getting a complete capacitor kit from Klondike Mike. He's a member here, and sells his kits on Fleabay. He uses good-quality parts and provides some guidance with his kits for getting the job done right.
But any project like this is a gamble. With the right tools and skills, you could zero in on the part causing the trouble. Re-capping the radio is a "shotgun" approach to the problem, hoping your aim is close enough to score.
The age of the radio should make re-capping the radio a 50-50 proposition. Might fix the fault, might not.
But from the way you describe it, I'd say it's probably worth the gamble.
73