Figured it out!! OK, I'm gonna explain this to everyone, because I had no idea what I was doing and had to do a bunch of guesswork and fiddling around, since the instructions I found weren't that clear and were a bit misleading. Here's a proper guide, so you all don't have to suffer like I did trying to get this to work. And yes, it's perfectly compatible with Sofarun, so you don't need to launch the game from the file manager.
Step 1: (only if you don't already have EP.COM) Download this zip file:
http://msxbanzai.tni.nl/computers/ese3.zip
Unzip it and go to TOOLS\DiskImage\EP.COM. Congratulations, you've found EP.COM. If you have one of those VHD's that Pezz 82 linked in his MSX video (That's what I'm using), then you already have an EP.COM file and don't need to worry about this first step.
Step 2: Create a batch file. All you have to do is go into Notepad and save the file with the extension .bat. NML32, the guy who made the YouTube video, said in the description to type something like this in the .bat file:
ep disk1.dsk /b
ep disk2.dsk
ep disk3.dsk
ep disk4.dsk /r
The "/b" is on the first disk, and the "/r" is on the last disk. "Disk1," etc. are just example names, make sure your names for these disk files match exactly the names for the disk files you're going to use. Also, make sure the "Disk 1" lets you start the game. For example, the game I'm playing, the English translation of New Devil Golvellius, only has the intro, title screen, and save feature on the first disk (GOV2ENA.DSK), and to start the game, I have to start with the second disk (GOV2ENB.DSK). So, what I did, was list GOV2ENB.DSK first and GOV2ENA.DSK second, so I can start from the disk that lets me start the game.
Step 3: Get your VHD and mount it with ImDisk. Make sure to register it as a floppy. Put the EP.COM file in your Utils folder, or wherever you normally put your command files. Then, put your batch file you just created, and all of your disk files to the folder you would normally put your game in. Finish the process by right clicking on the drive for your VHD and unmount it. One extra thing to note: EP.COM doesn't seem to like it when you put your game files in a zipped folder (when I tried it, it said it couldn't find the files), so make sure that you put your files in a regular, unzipped folder.
OK, we now have everything set up, so start up the MSX core and select the batch file in Sofarun. To swap disks, hold the F7 key, press the space bar, and then let go of the F7 key. If your keyboard has a caps lock light, it will probably blink when you do this. Then all you have to do is press the number for the disk you want to use, but subtract 1. So, let's say I want to bring up Disk 2, I hold F7, press the space bar, let go of F7, and then press 1. IMPORTANT NOTE: This only works when the game prompts you to swap disks. If you do it any other time, the disks wont swap and your graphics and possibly sound will get all messed up. So, make sure to ONLY do this when prompted to do so. Everything worked fine for me, both when switching to the first disk, and back to the second disk.
There. Probably the internet's first properly explained guide to how to do this. I'm not the most tech savvy, so if anyone is more knowledgeable about this stuff and knows how to do this more efficiently, please feel free to add to this. I wasn't sure what I was doing for the most part, so if I was able to do this, you can too. Have fun!!