How to get to New Game + in Fez

In the full game, there is a treasure map (you can look at both side of the map by rotating it the same way you change perspective during the game) explaining how to get there.

There is no ledge, even in the full game, only invisible platforms.

Not sure if the trial version has treasure maps though.

One of the coolest parts of playing Fez has been piecing together a story based purely on engravings and a smattering of owl and Dot sayings.

The only bit in the history you've outlined that I would take issue with is the bit where you say the big heads are ancestors to Gomez's people. And by big heads, I mean the ones running the successful stargate. I think the bigheads are the latest line in this string of creatures having heads large enough to contain information about the third dimension without shattering the hexahedron. They also all wear squares, or 2D cubes, on headbands almost as a religious or tribal identification.

I can't tell if the ruined city is in the past, or if it's more like ruins that the big heads discovered, or if it was a failed project that they relocated. There is some amount of time and space not acting as expected, beyond the established 3D gimmick, as when you enter the hut in the forest that exits in the mausoleum, or the underground place that is being rendered out of glitches.

Two tiny details that I thought were incredible: the tribal Gomezes live in 2 dimensional huts which they see with 1 dimensional eyes. They see in 2 dimensions because that's how many there are, while Gomez and the big heads have 2 eyes and can see in three dimensions, and the space squid have 3 eyes which presumably means they can see in four dimensions. This implies that the world was evolving as the creatures were.

Two final thoughts:

1. I think there might have been a second alien race or something. Throughout the game are skulls with three eyes, but laid out on a line, not in a triangular shape like the space squid have.

2. I'm not entirely sure why the one-eyes started worshipping owls, but in UFO lore, owls and aliens (in particular grays) are closely related. I have a friend who swears up and down he was visited by a talking owl as a kid, and the owl told him about the relationship between humans and aliens. It's as if, in the game, owls can straddle all the possible worlds because they can fly and see all the dimensions.