I have my two machines stacked. The Sony sits on the Phillips Recorder.
The drawers are in the same relative place on each machine and that means the lasers are only an inch-or-so apart. Is it possible that they are interfereing with one another? My problem, as I have mentioned, it picture "freeze"

No. Regulations prohibit any interference. If you separate them and think that interference is an issue, one is damaged. Also, it would probably not be the actual laser (RF or AC interference more likely), those are pretty low power.

OK, then let me think...I have the stuff plugged into one of those electrical extension cords that has the manifold of outlets (it's six, I think) I notice that the little switch, that allows you to turn the whole thing off and on, (which glows red when the thing is on) blinks as if it has a loose bulb in it or something.

As for RF, I think those on-at-dusk...off-at-dawn devices, you put under your bulbs in the outdoor light, throw off some interference as do the motion-detector security lights (at least they interfere with my AM radio reception, I think) I do have a few of them in my circuitry. Whatdya think?