The wash zone you describe is not suitable for very low recycle rates. If you mean valve trays and not bubble cap trays, those trays have been successfully used at recycle ratios of 15% and higher. If the wash oil rate is too low, the trays will dry out and coke.
The very high concarbon and asphaltene content of the HCGO indicates that there is poor contact between the wash oil and the coke drum overhead vapors in the wash zone. If these trays are coked, about the only way to restore the performance is to shut the unit down and enter the tower and clean the trays. You could try to increase wash oil rate and then monitor the HCGO quality. If it improves, you may need to operate the unit at the higher wash oil rate until the next outage.
Once the backflush filters have been coated with asphaltenes, simple backflushing does not reduce the pressure drop across the filter elements. Removing each element individually and soaking it in hot water to melt the asphaltenes off the filter may be required.
Good luck. Let us know how you resolved this problem.