So, what I had to do was to try and push all my hydroton/gravel to the other side of the bucket while attempting to not kill any plants, remove the metal-threaded bulkhead fitting, drill out a larger hole, and then install. I used 1" pipe this time, probably still not wide enough, but a major improvement. I've heard the occassional piece of hydroton getting sucked clean through, so I think the risk of clogging is lessened.
I also followed the recommendation of every single other aquaponics person in the universe and put in a standpipe with the cut out "V" at the top. I don't understand why that makes such a difference, but trust me, it does! The suction is now pretty impressive. I drilled plenty of holes through the standpipe to allow the water to fill in and drain out before it even gets to the top "V", and given that my water is running constantly, I found that the more holes I had, the more flow I could give the bucket without overtopping the standpipe and flooding the plants.
From everything I've read, people use the flood/drain system to ensure that the roots have enough oxygen to avoid root rot. Given that my pump is also operating the waterfall for my pond (more of an aesthetic purpose), I choose to let my pump run all the time. I find that the plants seem to do well enough that I don't notice the difference. Maybe they'd be even bigger if they had some time to breathe fresh air! Given that the water doesn't stay all the way at the surface, part of the root system is always getting some oxygen, so that should help.
My next system will likely be aquaponics only, so I'll try out a timer and do a flood/drain type of thing. I'm looking forward to not having to run the pump 24/7 from an electricity-use standpoint, as well.