I want to post my resolution to this. Took me some time to work through it so I might as well document it!
I ordered the Orifice Tube installer/remover I linked to earlier, turns out it is only a remover :(
That left me looking for Dave's tool:
I couldn't find it anywhere. So I went to Home Depot, and bought some 3/8 inch copper tubing. Yes, it is very soft, but I didn't want to apply a lot of pressure to the orifice tube anyway.
With a Dremel, I cut out slits for the sides of the orifice tub to go in, similar to Dave's tool. This is what I ended up with:
http://i.imgur.com/BTBTg.jpg
I slid this on the orifice tube such that it rested at the base of the filter, placed a piece of wood at the end of the tool and lightly tapped. Presto! Slowly but surely it slid in. It is now properly inserted.
I'm finally closing up my A/C system! Can't tell you how difficult that tube was to install without the right tool. Only took 2 minutes to install it once I had my homemade tool ready to go.