Yes it can be saved. But it isn't recipe simple, and may take a lot of patience and those soldering skills you mention.

I've been reading this list since 99 without coming across another instance of "intermittent poor FM solved by X" yet you clearly have isolated the region of the bad connection. The box you describe is surely the shielded phase locked loop tuner assembly, like the one in this CR712 , itself housing a circuit board with many more potential cracked solder joints. Mechanical circuit board intermittents are very difficult to find sometimes because the flexing is transmitted widely.

When you can't locate the actual crack, you can resort to reflowing every pad- not that big a project if you've truly got the region right. It can sometimes help to use a meter to look at voltage in random spots while flexing the board, in an attempt to localize the effect, even though you have no schematic.

Ninety out of a hundred would use this opportunity to spend money on an updated unit, but I'm one of the ten who keeps the old originals going.

--
Art Benstein near Baltimore