I'm trying to make a map that makes sense to me for use in my fan-fic and for the next time I run an rpg in the Trek verse. So I want to include certain novels, the Triangle, and some of the other non>anon material.
You could try making all three empires completely non-contiguous.
That "Federation space" is just a sphere about 20ly in diameter around a planet/system that the Federation has claimed and/or colonized and everything else is "interstellar space" that no one can legally (or feasibly) claim to control. If you also add a a certain interpretation to interstellar law that basically makes "unclaimed" space a kind of lawless free-for-all, then starships from opposing fleets can do whatever the hell they want in the interstellar regions without worrying about the political blowback; it becomes a "declared war" when they violate the territorial claims of those choice systems, which is why the Federation and the Klingons (and also the Romulans) only ever come to blows over planets that BOTH sides want to claim for themselves.
In that sense you could think of "Klingon territory" as generalization for "systems the Klingons own," and you can't really know exactly where this is without looking at the star chart for your local area. That would also explain why we have such a hard time understanding where the Klingon and Romulan empires actually are; they literally are EVERYWHERE, just like the Federation.
I assume the UFP has a core, actual border, and a treaty exploration zone that has nodes of colonies, trust worlds set aside for worlds not yet in space, and unexplored space.
Why hold that assumption at all? Even in maritime law, it's become convention that you can really only claim territory (waters, airspace, etc) that you can feasibly control. If you can't control it or exclude others from using it, your claim on that territory is meaningless.
When you consider how thinly distributed and far-flung Starfleet really is, it's simply infeasible for them to actually claim huge swaths of interstellar space and say "Mine!" despite the fact that they cannot realistically prevent alien ships from entering those regions (and in most cases, may not even realize those regions have been penetrated). If, OTOH, "Federation space" only exists in the area around "Federation Worlds" then it isn't a matter of distance or proximity; you may have two colony worlds with a million people on each, and somewhere in a 200ly gap between them, five unexplored systems that get a visit from a galaxy class starship. Suddenly we're not scratching our heads wondering "How did the Enterprise manage to answer a distress signal from that huge Federation colony when it's supposed to be exploring the uncharted regions of deep space?"