I burned Shin Megami Tensei: Persona 3 with ImgBurn 1x to a DVD-R (Sony), when I tried swapping it with Swap Magic 3.6, the screen just goes black, and doesn't load.
First of all, you shouldn't be burning at that low a speed. Most of the time it's best to burn at 4x-8x (depending on your burner and discs). If you have a decent burner (with the latest firmware) and a good computer, a good rule of thumb is burn the disc at half the max speed mentioned on the disc.
It could also be some bad media. Check this thread if you want to know more about that possibility.
While these thoughts may or may not help your current situation, they're certainly good to keep in mind for future reference either way.
Well, the first post in that thread I linked to will tell you what media is good (Taiyo Yuden is the simple answer). Get some 8x or 16x silver backed ones (not the printable ones, unless you *really* want to print labels onto your discs) from one of the sites mentioned in the first post if you can, as they are overall cheaper than buying crappier brands in an actual store, and they'll be much better to you and the laser on your PS2.
As a note, DVD+R discs are good if you have a v7 PS2 or newer (some say v4, but it seems that DVD-R are still better up until about v7) and you know how to bitset the discs. If you don't know and don't want to bother trying to figure it out, just get DVD-R discs.
With the speed of your drive, 16x media are best burned at 8x. Just make sure you have the latest firmware. Never burn below 4x for a drive like that (well, unless you have 2.4x DL DVD-R discs or something like that, but that's a different matter...). Many people with newer drives have actually reported problems when trying to burn at speeds below 4x, so that could definitely be the problem here.