Title, I tried converting the coordinates from here to rectangular but it seems off.
At the bottom of your linked web page is the sentence:
If you need really accurate data for a planet or asteroid, try the JPL HORIZONS System. (These guys were navigating spacecraft through the solar system when I was still playing with GI Joe!)
...which is indeed an excellent answer to your question!
A step-by-step example of how to obtain "rectangular coordinates of the solar system planets" using Horizons can be found in this answer.
I could not find a good live imagery of planetary positions. Also try this question in Astronomy SE.
The examples in the question and the comments are valid ways to track the planets. I do see plausibility in converting the coordinates into a visual grid.