ditto, blast some co2 through the liquid line. they make filters that you can install on the dip tube, they seem to be more problems than benefits though.
the other option is to crank the co2 up to 30psi or so and see if you can force it through.
counter pressure filling will run into the same problems, and as oginme stated, racking it off to a bottling bucket is going to add o2 which is going to kill the beer. I find with my IPA's especially NEIPA's that ANY... I mean ANNNNYYYYY o2 really kills the flavor and appearance.
I would suggest if you're going to counter pressure bottle, first blasting co2 through the liquid line, then tilting the keg to a slight angle when bottling should help reduce hop sediment from clogging it up again.
making sure you get a good seperation of hops when racking to kegs eliminates the issue for me though. I use a conical and make sure to NOT get any hop sediment when racking to kegs. you still get that nice hazy look without getting actual hops in the keg.
Good luck!