First a very important question:
When did you get EBV?
EBV is almost certainly the major cause of your candida. EBV/glandular-fever is very tough on the liver and after battling the virus for an extended period of time the liver can be left sluggish and unable to produce enough bile to complete digestion. As a result food rots inside the intestines instead of being digested properly, thus inviting opportunistic pathogens such as candida and other dysbiotic flora to have a field-day.
As you have astutely discovered your health problems are not disconnected.
EBV can be tackled with 2 things. First there is a product called Elbucol/Sambucol which is made from Elderberries. This has shown to help the body fight the virus, but since it is high in sugar it may not be the best thing for you. Second coconut oil is deadly against lipid coated viruses such as EBV. I haven't verified this myself as I didn't know about coconut oil when I had glandular fever. But I have tried coconut oil on cold-sores (herpes virus) and it works like a charm. 100 times better than the commercial ointments such as zovirax which don't really work at all. Coconut oil also has the advantage of being anti-fungal so will aid your battle against candida.
My story: I got glandular fever (EBV) 3 years ago, then developed what I thought was CFS. A year ago I realised I had candida.
As you point out the yeast may well come back (eventually) if you don't get the virus under control, becuase an overactive EBV will always weaken your liver, which will mess up your digestion ...
As you point out the main thing is to get your candida under control using liver flushes to strenghen your liver. I would also recommend liver supporting herbs in between flushes such as Planetary formula's "Bupleurum" and Dr Sandra Cabot's "Livatone Plus".