This is pretty interesting actually. Jund Panorama or Marsh Flats can search this up but they can't search up Island; same is true of Korlash, Heir to Blackblade, Corpse Harvester, etc.

While interesting, and indeed deserving of a Basic land type, there's no way this should actually have the supertype Basic. In no way does it feel Basic.
You can't mess with Basic lands. Adding a supertype like Snow (or Day and Night, like in my Dienoct set), which has rules meaning and was practically integral to the function of Snow permanents, is one thing. This is totally different.

What I'm trying to get across is that the basic, fundamental Forces (aka the basic lands that produce mana) themselves have been warped due to time travel shenanigans. Right now I have 20 basics in the set, 10 of which are like this (2 normal, 1 enemy, 1 ally). Another thing is that if these are not basic, then I'll have to hollow 10 common slots, which is quite hard in a small set.

Noted on the Untainted Lands. I'll see what I can do with that.

But the Breached/Warped cycle... I donno, I just really like the fact that you don't need to only have 4 of these in a game. You can literally play mono-blue with 24 swamps.

I don't have to agree with you in order for you to do what you're doing. These can be basic if you want them to be. I just really, really don't think they should be.
That said, I do sort of like this note that you've removed the Basic supertype. I would flip the border color and the big symbol, though, to make it more obvious that this taps for . The ability also needs to be worded as a replacement effect rather than a triggered ability.

A clue on how I can word this?

I like the fact that even with Chromatic Lantern, you can't tap for , even thought it's a swamp. It fits with the new primal forces 2.0, "Revenge of the Legendary Nephilim"