Fridge moved now too cold, should I install a timer to limit run times?

I am an American living in Perth Western Australia for a year. I bought a used fridge just a short distance away. My covered truck wasn't high enough, so I laid the fridge on its side. (I've read your fridge moving advice on the web site -- I don't know if I laid it down with the suction line downward). Then to compound matters, I think I plugged it in very shortly after moving it.

Since then, it still runs great, except TOO GREAT. Even with the temperature set at the lowest level, things in the fridge compartment freeze over within 6-8 hours of turning it on. We tried turning it off and letting it sit for a 36-48 hour period, but the problem persists. Will the problem be corrected by letting it be turned off for a longer period?

We do not hear any noise in the operation, so at least maybe there is no spring damage. If the refrigerator oil has gotten into the high side lines and we have to have the capillary line blown out, is this a costly procedure? Will it consume most of the value of the fridge??

Suppose we hooked the fridge up to a timer, so that it would run for 3-4 hours, then shut off for 3-4 hours. This would end the freezing problem for the short term. Is there any chance the refrigerator will return to normal operations eventually?

FYI the Fridge is a Kelvinator model, freezer on top, fridge on bottom. 500 liter capacity, The compressor says it is made by Matsushita in Singapore.