Thank you caffeine, I didn't know whether to laugh or cry at some of these responses. The scale that I'm using is no different in principle than so many other scales used in other scientific, and non-scientific disciplines. What it is, is a method of model building, it's often done in biology, and seldom if ever done in astronomy, simply because of the preferences of those who control science. In biology, it's done to bring microscopic things up to a size that humans can analyze and work with. A scaling up. Scaling down does the same thing, as one example - building plans are scaled down, many/most commercial building plans are drawn to a scale of 1/8" = 1'. Working drawings (building plans) are another way of 'model building'.
I remember seeing something in a news paper long ago, about a science teacher who built a scale model of the solar system. I think he used a beach ball as the sun, and a pea as the earth, if I remember right. I think the planet Neptune was a baseball, several miles away. A school bus was his class's spaceship! This teacher probably got fired, I'd say many of his students never forgot this lesson. They're the types that , like me, would probably question "facts" that they hear about events happening thousands of light years from earth.
On the contrary, astronomers seem to me incredibly fond of using scaled down examples to explain to people the incredibly vast distances they have to deal with. Every popular astronomy book I've ever read - all written by evil evolutionist scientists - has contained some analogy along the lines of 'If the sun was a melon in the middle of Sydney Opera House, then the next nearest star would be in Newcastle'. There have been several projects, such as you describe, to model the universe to scale. There's one along the waterfront in New South Wales,and I was reading about another recently somewhere in the US, where the sun is in a local museum and the outer planets a few miles' drive away.
Here is one of many scale images on the internet - it's mostly just an enormous blank page.
None of these scales are some dirty secret the scientists want to cover up, because they don't pose any of the problems you claim. On the contrary, they're a source of fascination and wonder that astronomers are fond of describing.
You haven't really explained to us why this huge distance is supposed to be a problem. If we're on earth in your analogy, we're trying to see around the curvature of the planet, past all the intervening stuff blocking your view, and through an atmosphere - it's not possible. If we stick a telescope in space, however, looking straight through the inky blackness without anything in the way to obstruct our view, things are much simpler, and the parallax angle is measurable for stars up to about 100,000,000,000,000,000 miles away, your personal incredulity notwithstanding.