The dummy dataset I provided didn't represent the real issue in my data well (my bad). I have resolved the issue with my real data taking the following steps:

1. My qPCR was run in triplicate for each sample so I had 3 species estimates for each sample. I took the mean of those three estimates.
2. I ran the above model with autocorrelation specified as: acformula(~arma(time = seq, gr = species:site, cov=TRUE)