So here's a little update. I spent a number of hours messing around with various codecs and programs. I managed to get some fairly decent results. I still kept having various hangups with the conversion of a file from variable frame rate to constant frame rate. Mostly, I had trouble finding settings that would preserve transparency effects. I kept getting results where the flickering sprite would be solid for a little bit, then turn completely solid, then disappear altogether. Since I am still in the "just messing around" stage, a high powered capture card like the SC-512-N1 isn't on the menu yet. A card like that would necessitate a raft of upgrades that I don't want to deal with right now either.
I noticed that the new ElGato HD60 records in constant frame rate. I have one of the old Live Gamer Portables from Avermedia that I used to mess around with, which is okay. The PC free recording mode was kind of cool. The software is kind of crappy though. I had an Amazon gift card laying around so I went ahead and grabbed the HD60.
First, it does indeed record constant frame rate, which meant I no longer have any audio de-sync issues with Light Works. At first I was surprised that the files didn't seem to be too much larger, but the way the ElGato software handles the bitrate is different than the other software I was using.
So I wanted to make a test clip to see how well the transparencies are preserved. In the source clip, there is only one instance where the sprite of the old man flashes a little brightly, but other than that, the effect is preserved perfectly. After being rendered in Light Works and uploaded to YouTube however, things got a little messy. You can see what I am talking about during the cut scene. Be sure to watch in 60fps if you are on Chrome.
As you can see, there is quite a bit of flashing and drop out going on there. I haven't really done any tweaking of Light Works settings, so I am going to look at that next.