Cruise Control Intermittent Issues

Based upon your post, I would have to say your engine is in amazingly bad condition - or else you have a very low threshold to be amazed.

1. You are right that DTC P0420 means that the catalytic converter has failed. There is no point in replacing it as long as the engine continues to burn oil at an accelerated rate.
2. If the engine is using one quart of oil in 400 miles, it is seriously worn out. What is the odometer reading?
3. No surprise that the fuel economy is poor given #2 above. A worn engine is converting more of the chemical energy in gasoline into heat energy (due to abnormal clearances between the pistons and cylinder bores), instead of into mechanical energy which powers the drivetrain.
4. If the cruise control is not working, that probably means another DTC has been logged which was not reported to you, having to do with the hybrid drivetrain. Another possibility is that the cruise control switch or the spiral cable is faulty.
5. You cannot get around the fundamentally poor condition of the engine, plus who knows what else is wrong with the drivetrain.
6. What to do: get rid of the car. It is probably not economic to install a used engine unless you can DIY. If you could DIY you probably wouldn't post these questions...

 

The failing catalytic converter condition is unrelated to the non-functioning cruise control. The cruise control is just a software function in the hybrid vehicle ECU. If the cruise control is intermittent, either you have a problem with the cruise control switch in the steering wheel, the spiral cable in the steering hub, or the HV ECU is refusing to activate the cc.

Considering the high engine oil burn rate, don't expect a new catalytic converter to last very long.

 

I suggest that you need to find out what are the current DTC being logged by your car after you replaced the 12V battery. Mini VCI is an excellent means to achieve that if you have access to a Windows XP or Windows 7, 32 bit OS.

If DTC C1242 is still present, then you would need to check the ABS1 and ABS2 relays as well as the wiring harness leading to the skid control ECU. Either could cause a problem with the hybrid vehicle ECU inhibiting cruise control operation.

Hybrid vehicle ECU failure is very uncommon and you have not reported a DTC associated with that, such as P0607.

 

Do all the other buttons on the steering wheel work? Specifically check the ventilation recirc button, as it's often the first to go when the spiral cable goes bad.