Hi Leemh, Regarding the pitch shift issue I am suggesting it is an artifact based on the very nature of how all pitch shifting works. So in short there is nothing wrong with your JTV and a replacement board will likely behave the same.
As in your video my JTV behaves this way as well with certain tunings especially when higher strings are tuned low. I can also achieve the same artifact if using a pitch shifter plug in on a single string e.g.: in my daw (Logic).
So should you get a replacement? If they are doing this no charge I suppose there is no harm other than your time.
If you are doing delicate recording that requires the best quality I would simply tune the actual strings to the open tuning of your choice for the best results. However if you are playing live in the context of a band or your recording simple demo's the effect will not be too noticeable.
What Line6 have achieved in low latency is amazing coding for sure and perhaps the tradeoff is the pitch shifting algorithm? Considering the JTV series has 4X the processing power of the Older series it may be there is more improvements to come? Who knows...
Roger