Thanks everyone for your input. The old seal(s), looked much like old Chevy front wheel bearing grease seals, only with two of them installed. I installed the new seal pressed in just far enough to get the clip back in. It did look a bit strange with all that open area behind it, but Honda had verified that it was the right part.
After I got them in and put the sliders on the new fork tubes, the bolts (in the bottom) wouldn't tighten up, even with the forks compressed. I took them back off and cleaned the residual fork oil from the mating surfaces using carb cleaner, put them back on, and they tightened right up. I finished putting everything back together, added fork oil, and took it for a test ride. Everything worked great. The front end was nice and firm and, after about twenty miles nothing had came loose and there was no leakage.