The coils should all get cold. If a system is low on freon it
could have a small leak and should be completely serviced before
re-installing the inner liner.
       
      When ample new fiberglass insulation is installed, it will push
those cooling coils pretty tight against the front and rear walls
of the liner.
 
       I don't think the original copper coils were really soldered
to the galvanized tank, they just used a lot of tar.

It originally took R12, between 9-12 oz. depending on the compressor model.

If you don't have the equipment, you'd best leave it to a pro.