The simulation is showing that the discretization method impacts how the PLL performs. The default discretization method in PLECS for your continuous model implementation shows the additional gain at 60 Hz. There are many references on different discretizaiton methods and several papers on discretizaiton approaches for the SOGI PLL specifically.
Researching this and choosing the correct approach is an engineering decision on your part. PLECS will be helpful in analyzing how the different approaches perform in both the time and frequency domain.
I’d recommend using the wrapping integrator as you outlined. I can’t comment on the problem you noticed, but if the error got worse over time, then the floating point value accuracy could be the cause.