AFAIK FTTP backhaul is completely different to FTTC, so upgrading for FTTP should make zero difference to FTTC.
Did you mean to say that? It's different so makes no difference?
It depends on the backhaul provider but generally the backhaul is identical between FTTC & FTTP.
The only difference in latency between the 2 is what is added by the DSLAM.
Is the change in ping time to do with G.INP parameters changing? Can you see those stats?
G.INP adds no delay.
It's INP+Interleaving that adds a minimum 8ms on FTTC.