my only concern should be with the unreal single player maps, as the mod would require me to distribute all of them for the player to be able to play through.
That's a big problem. You're really going to have to be clear here. Are you trying to make something using unreal that people will be able to use without legally owning a copy of unreal (lets pretend warez doesn't exist) that they bought in a store, ebay, from the totally unreal package, etc? If so, then what you are planning on doing is almost certainly illegal. It sounds like you are trying to use the unreal engine to make a 'movie' viewable to people without having the game (i.e. so they can preview what it's like; a trailer that shows the entire product). To do something like that you would have to get a copy of the unreal license from Epic. I have no idea what the procedure for that is (and UE1 probably isn't even available for sale anymore), but it would certainly cost money.
Now, are you sure you aren't just horribly confused about this whole thing? Your 'problem' of having to distribute the single player maps is such a big red flag to me because if you're making any kind of real mod that runs in unreal, there's no need to distribute the single player maps, or any of the content (on that note, the maps are next to useless without also giving out all the textures, sound effects, and music files). If it's a "mod" in the traditional sense, like everything on that page, then it requires the user to have a copy of unreal, and thus they'd obviously already have the single player maps. Or maybe you just think a mod needs new maps? That's certainly not true. Only a few really big mods on that page (RealCTF and Infiltration to name two) have their own map packs. Unless they significantly change gameplay, like RealCTF does, there's no
need for new maps. Most just work file on the original deathmatch maps or custom maps that people have made over the years. My Hide and Seek mod mostly just uses a handful of the single player maps, so no it isn't restricted to the deathmatch maps. I already said that you're free to reuse any of the content that comes with the game. This does include maps.