I have processed many materials at these temperatures. You must make sure the plastic itself is at the right injection temperature and the time sequence is not too slow for opening and closing the injection mold between cycles. For the injection mold I would use plastic processing equipment controls for cartridge heaters and thermocouples. These are much more efficient than using oil heaters. Make sure the heaters are within a .25 inches from the injection mold surface and space the thermocouples between the heaters for accurate readings. To cool it faster use a water jacket system with a closed loop to conserve water. This can be designed with common off the shelf plumbing supplies. You can even create an outside retention pond that will add cooling value and looks really awesome outside your facility.
Electric heaters with on-off controllers will be a problem unless the injection molding cycle matches the heating cycle (unlikely), but you can use a variable-resistance (like a dimmer switch) to keep constant voltage (value set by you when you see what works).
I run into this in extrusion — with small controlled dies, we get “hot-lips disease” which is thickness fluctuations in time with the heating cycle. It is possible to undersize heaters, but that is a lot of guesswork, and with minimally-insulated dies, even night-day cycles cause trouble, hence my preference for taking the die off control and on to a variable resistance which can be adjusted by the operator as needed.
No-one has mentioned mold cost yet, but if mold is not made yet there is a decision there. I suspect oil circulation is more expensive, especially including pumps/heat exchanger, so decision ultimately depends on expected quantities and product sale price.
The key factor to maintain an injection mold temperature > 200C is the thermal insulation of the injection mold to its surrounding. The heat loss to the surrounding air and connects are so huge making the controller difficult to compensate. If you can properly insulate the mold, not overlooking the piping in and out of the injection mold, you should be able to keep the temperature at the set one even with a less sophisticated controller.