Hi and welcome,
I am sure that you are correct when you determine that the 300w PSU is the cause of your problems. From what you have told us I would suggest a PSU of 650W minimum. Make sure however that you buy a good quality one from a respected manufacturer like Seasonic, CWT, Corsair, Thermaltake, Enermax, Gigabyte, Coolermaster, Antec, etc and try and get one with a single 12V rail if possible.
It is easy enough to swap the two units and if you purchase a modular type it is even easier as you only connect the cables that you require which saves a lot of unused wiring lying around.