Failed attempt to swap temperature control modules

Help, I have questions on thermocouples and temperature controllers. I need to pick you brain on how these things work. My oven originally came with a Syscon rex-c100 temperature controller that displayed in Celsius. It had an internal 12 volt power supply to run the relay for the heating element. I replaced it with a controller that displayed in Fahrenheit. It did not have the 12 volt power supply so I have red necked the unit to use the power supply in the rex-c100. I wanted to clean up my mess so I reinstalled the rex-c100 but the internal temperature is incorrect. I am thinking that it wants a K type thermocouple, the thermocouples in the over are J type. This would mean that the oven was shipped to me with the incorrect thermocouples. Fee bay lists the off brand name rex-c100 at a very cheap price, https://www.ebay.com/itm/Digital-PID-REX-C100-Temperature-Controller-40A-SSR-K-Thermocouple-Heatsink/292350306904?epid=801740921&hash=item44116faa58:m:mxNEvQQmAa932FS4g0U-dxw Fee bay only list pre-owned Syscon Rex-c100 and the prices are quite a bit more expensive, https://www.ebay.com/itm/Syscon-Rex-C100F801-M-AN-Temperature-Control-100-240VAC-Range-0-0-100-0/182776175634?hash=item2a8e4f1c12:g:kGIAAOSwLyVZwRxj New ones are very expensive. https://www.galco.com/repair/Syscon-RKC/REX-C100 Is there anyone out there that is willing to talk to me about this? I have swapped everything back an the replacement control module does control the internal temperature correctly. It is a J type thermocouple.