Pace over the years made a few changes to their desoldering irons to minimize blocking problems. A short high suction burst after activating the button, extending the vacuum run time a little after the button is released, extending the heater and fluting the back ends of the tips. This means the solder is more likely to clear fully on the first burst, less likely to clog because a too short vacuum duration was pressed and the vacuum path minimizes cold solder buildup.
I've included some videos to watch for pointers on technique. So ensure your desoldering temp is high enough not only for the joint but the desoldering iron, freshen the joints before desoldering, ensure the tip heats the joint fully before sucking, increase the button press duration to clear solder, and wiggle the pins while desoldering so that maximum solder is removed. Avoid applying tip pressure into the PCB as this disturbs the pads bonding.
Try using minimal flux as you will be sucking it into your desoldering iron decreasing airflow and creating additional buildup. For maintenance empty the trap before significant buildup and performance is degraded. Change the primary filter more often for max airflow. Use the tip cleaner more regularly.
One difference between Pace tips vs your Hakko model is the entire shaft is replaced when you swap over the tip, this helps with reduced wear. Abrasive cleaning eventually leads to wear and will cause solder to recatch. So you may need to eventually replace the back part that is getting blocked.
As a last ditch effort once everything else has been tried I might be tempted to use a super light high temp lubricant. Just a trace amount at the bad end. It's a bit of a juxtaposition because you want to loosen up flux and solder buildup with an abrasive tool but you want the inside of the shaft perfectly smooth so that nothing can catch. Edit: I see that it might be part of the heater, unfortunately.
Watch 00:20
Watch 43:46