I just had a thought, the transistors of a zenith 755 are mounted in sockets like vacuum tubes. Pull out all of the transistors and carefully label them to where they go and what number they are. Then apply correct voltage at the right polarity, with a current meter in series with the radio and see what the current draw is. It should be next to nill. if it isn't then you know you have a shorted cap, transformer etc. If no current draw then start replacing the transistors one at a time and see if anyone of these cause excessive current. i found the schematic for a 755m and it says the current should be 17.5 milliamps with the volume turned down but still on. also there are 2 electrolytics connected just after the power switch. they would likely be the best candidates for drawing enough excessive current to drain those batteries in only one day. here is a link to the schematic i found.
https://radiojayallen.files.wordpres...ce-manual1.pdf