The impact of spatial referencing from time-series to time functions estimation (velocity) is known, however, it's unknown (to me) of its impact on the network inversion.
If you want to plot a map or time-series with a different reference point rather than the one used in the processing, view.py and tsview.py have the --ref-yx/lalo option for it, so no need for re-processing.
If you do want to re-process the data, then I would recommend to re-start from the inversion. It will be difficult to remember all the inconsistencies in the setup in the long turn, based on my persona experience. I ended up re-process it anyway ;)