[Arran]

Here is what I would do, but only as a last resort, make a diagram of where everything is connected to that bandswitch, coils, wires, resistors, condensers, etc, then disconnect everything and remove the switch. You can then work on the switch without anything getting in the way. There are a couple of things you could try, I would wash it with a TSP solution to get rid of the dirt, then I would soak the assembly in Varsol to dissolve any old grease,clean the Varsol out with alcohol, then oil the bushings. Another thing you might try is tuner bath or carburettor cleaner. If it still won't free up then you may have to disassemble the switch, which is not always possible. Replacement often isn't a viable option especially with the stacked wafer affairs, in almost every case you will have to find a replacement bandswitch from a junker chassis, generic replacements generally won't work.
Best Regards
Arran