We had this problem. I kept trying to fiddle with the purported
self-leveling mechanism with no real luck. I finally broke down
and grabbed a few wood shims from my inventory (about $1 for
20 or so). I raised the level of the front of the fridge until both
doors closed well on their own. This was less than one inch.
I know this isn't the most sophisticated cure for the problem,
but it sure was quick and worked for 29 years.
That fridge finally died last week! Total cost of repairs for 29
years was $3. I laughed when the salesman for our new fridge
tried to push the extended warranty! Of course, we were
extremely lucky with our old Philco fridge.
When it failed last week, I messed with it for an hour or so and
could determine that (1) the timer for the defrost cycle wasn't
moving and (2) even when I cycled the timer manually, the
compressor wouldn't kick it. I'm guessing that I could have
found a loose or corroded AC connection somewhere to explain
the two problems, but the wife was rather eager to hear me say,
"It ain't worth spending more time trying to get a 29 year old
fridged to work. Let's go out tonight and buy a new one"