Shifting AC Signal for ADC
I can't add a DC shift centred around 1.65V before passing it through the PGA, as this will also amplify the DC shift


Yes you can, and you have to. The PGA you want to use, MCP6S91, can only operate on positive signals, centered around a positive DC reference voltage. It has a dedicated VREF pin for this exact purpose.

There is even an example in the datasheet for a 2.5 volt DC bias: