The radio works fine on BC but on SW the oscillator does not run. From the schematic it looks one coil is used for the BC oscillator and another coil is put in parallel for SW. In BC the coil reads 5.6 ohm. In SW the resistance drops to about .5 ohm. Does this sound reasonable for a SW oscillator coil?

I'm not certain.. however, logically ...the higher the frequency the smaller the coils.
Small means less windings and less resistance.
I don't think they would put the two coils in parallel.
Check all the switch contacts and all your connections.