I'm not familiar with the T962A or its controller so I am commenting largely in ignorance. However note that the ControLeo2 uses an open-loop temperature control technique and only has 1 adjustable setting for reflow (without hacking the source code) - the target peak reflow temperature (unless I've missed recent updates to the code). It may be perfectly adequate for your needs, or you may find it lacking if the T962A's stock controller offers any kind of sophistication.
ControLeo2 will run on an Arduino and it's easy enough to get one running to give it a trial - my DIY oven currently runs it on an Arduino clone, with a DFRobot style LCD/keypad for display and control, a Maxim SPI thermocouple adapter and a triac + opto-driver for the heater element control. Of course it's easy enough to use OTS Solid-State Relays with logic-level inputs for the element(s) control. To get that running just required adapting the code to the keyswitch input and the thermocouple adapter (from memory).
What is it about the existing controller that leads you to call it inaccurate? I know I'm not overly happy with the current behaviour of my setup. I use a separate thermocouple-based temperature meter to compare with the ControLeo2 temperature, and the two are rarely in agreement. In particular with a reflow peak termperature setting of 212C the meter gets to a peak of 225C, while the ControLeo2 peaks at about 215C.