So, after a lot of trial and error with a ton of different software utilities, I finally managed to get the video files off of the DLII Blu-Ray converted and working in Daphne.
For anyone wondering about the difference in quality, here are two comparison pics.
The Laserdisc rip provided by Daphne:

And the HD Blu-Ray rip:

The HD image is much brighter, cleaner, and with more accurate colors. Worth the effort in my opinion. The Daphne boards claim that the LD rip is the best quality out there, but I have to disagree.
If anyone's interested, here's the 5 steps I followed. This assumes you have a working Daphne DL2 installation.
1) Rip all of the .m2ts files inside the /BDMV/STREAM/ folder of the blu-ray disc to the hard drive. I used
DVD-Fab, but
MakeMKV and others can do this too.
2) Open up your Daphne folder with the laserdisc-rip vido files, alongside the folder with you new HD files. If you set your view to "Thumbnails" you can tell at a glance how to match them up. You need to manually rename each of the HD files to the same name as the ones in the Daphne folder. This sounds awful, but it only took a couple of hours total.
2) Use
Handbrake, along with a separate tool called
BatchEncoder for Handbrake, to convert the ripped files. This part was the trickiest to figure out.
Use the following settings in Handbrake:
File type .MKV; video codec MPEG-2; framerate Same as Source; Avg Bitrate 8000K; audio codec Vorbis; audio bitrate 192; audio samplerate 44.1.
Also, note that the HD video files come in both 4:3 (with black bars) and 16:9 (stretched with some loss of image) aspect ratios, but both are in the full 1920x1080 resolution. For best results in Daphne, you want to crop 240 pixels off the left and right side to eliminate the black bars, and you want to have Handbrake resize the (now 1440x1080) down to 640x480.
3) Use a demuxing program to split your new .MKV files into a matched pair of MPG/OGG files. I used
MKVExtractGUI2, but there are others that people have used.
4) Use
Bulk Rename Utility to change the .MPG extension to the .M2V extension so Daphne can play it.
There's probably other ways to do this, but I thought I'd share what worked for me. It really makes playing it on an arcade monitor a lot more fun.