Almost anything can be repaired if you work hard enough at it.
There's lots of info online on the 10811 oscillator, including full schematics, so repair is possible. The 60159 version is a bit rare, though. I see that one is for sale on ebay. It looks like the unit is soldered shut. That will make repair a pain. Unsoldering oscillators is a bit of an art. Do it wrong and you overheat the interior.
The first step is to pull the oscillator and power it up on the bench so you can do some testing. Check obvious things like current draw, frequency while warming up, response to EFC voltage, etc. Confirm that the fault is in the oscillator rather than the 58503A. You mentioned power supply problems with the 58503A. Maybe the oven isn't getting any power.
Ed