If all the diodes where bad you would have many more problems than you're having. I think there's something wrong with the readings, but not sure what.
Closing the switches shouldn't make any difference on the readings you get. You could always lift one side of the diode and test again to make sure, but this really shouldn't make any difference.
As a side note there is no reason to close the switch when taking readings.
Old games often have corrosion on the leads so make sure you've got good contact on the diode leads.
A beep would indicate a dead short and the diode is bad, but again I doubt they're all bad.
The .3 to .7 is probably ok, though not sure why you would get that much variance between diodes. The .001 or .01 would indicate bad, but again I don't think they're all bad.
In regards to the 1.1 reading, is that the null reading on your meter? Turn on the meter, switch to diode/continuity and the reading on the display will be null for your meter (it's different on different meters). Null means open.