Agreed, jumpering the switch is a bad idea; you can easily run the compressor without oil (as the refrigerant charge distributes oil).
You said you have 12V across the pins of both pressure switches but not at the clutch? Typically, the ground for that circuit is on the other side of the clutch from the switches; without the clutch connected, it shouldn't complete the circuit at the switches.
I'd definitely get a set of gauges on it and confirm the pressures, but also look at the clutch itself. You can measure resistance across the clutch pins (should be something like 3-6 ohms), and look for damage to the clutch hub (if the gap between the hub and coil were too large, the clutch wouldn't engage). You could also apply 12V to the coil to see if it engages.