I find it hard to believe that a dead fish stuck around for three months without getting eaten by CUC and/or decomposing, so it likely died more recently than that. Maybe it was hiding for a while before it died? In any case, a dead fish and dead CUC would definitely add nutrients into the water. My guess is you are reading 0 nitrate because the cyano is consuming it before it builds to a detectable level. Often, these problems take several weeks or months to develop, and it can take that long to resolve them once you know what the problem is.
If it were my tank, I would increase the water changes -- maybe 10% every two days, siphon out any visible cyano as it appears, cut back on the feeding to once or twice daily, and make sure the lights weren't on longer than 6 hours or so per day. Then test your nitrate and phosphate every day. If you keep removing the cyano, your nitrate should start being detectable and phosphate will likely increase -- then the water changes should bring them down again. Keep at it for a few weeks and see what happens.
