It looks like there is a absolute timing dependency between the DATA_P and DATA_N signals, are you sure that you will be able to interpret the data correctly with the PIC controller? Is there are way in a PIC controller to get a timing relationship between two captured serial streams?
Right and there is result pair per ASIC, that's a lot of data for a micro analyse in real time. Perhaps a CPLD in front of the PIC would be smart?