I would continue with the Protozin, if it is an "ectoparasite" then it is most likely protozoal and Protozin is a good med for that. If it is Lymphocystis, I'm afraid that there isn't really an effective treatment. Is the fish isolated from the rest of the tank? If at all possible he should be quarantined, that should be easy enough with a Betta. Either of your possible suspects can be quite contagious and it will be cheaper and easier to medicate a smaller volume of water. Some people have had luck with surgically removing the tumor from the body and /or fins but I don't know that I would advise it. The lethargy that you are seeing could very well be related to your nitrite levels. I would do a 30% water change and re-check. It is a little worrying that your nitrates are zero, most all well-cycled tanks will have some nitrate. Have you changed your filter-media lately? If so, you could be experiencing a mini-cycle which could have led to stress on the Betta exacerbating his condition.
You edited your post while I was taking too long typing a reply, lol...
As for isolation... I don't have the means to isolate him in a heated, filtered tank. I have an unheated, unfiltered 14L tank which is currently reading 21C with Poly-sponge to keep chemical levels reasonable, but am worried that the shock, even with gradual acclimatisation, could finish him off!