Your circular saw should be able to cut the 45 degree angle, there should be a lever to allow you to tilt the plate thus tilting the bade. Something like this
Then to get a Straight cut you need a guide along one edge. You need something longer than the piece you are cutting and wide enough to clamp it to it and have enough room to run the saw along the edge for a straight cut. Something like this, although this is a special clamp guide, you could just use something a bit wider with some other clamps.
The Easy Way
Fortunately, you're holding up a model train, not an actual train, so you can take some liberties.
The hard part is following the rounded, off-square corners; the easy way to work around that is to literally cut corners. Rather than attempt to follow the rounded corners, just install four shelves as long as the straight parts of each wall, then measure and cut four trapezoid shaped connectors for the corners. Just about any method would work to join the trapezoids to the main shelves since there's not much weight to support. You might use pocket screws, maybe half lap joints if you have the router etc. available.
The Hard Way
You could do some geometry, measure diagonals, get out a protractor, etc. etc., and find the angles. You may even be able to use an app that works with your phone to determine the layout. But in my experience these things don't end well :)
Here's how I picture doing it ... be warned, these things don't always work the way I pictured it.
Install your shelf brackets first
You'll want to rest the shelves on the brackets as you figure things out. I'd place them all on the straight (not rounded) part of the wall, but try to get one as close as possible to the point where the wall starts to round.
Make each shelf as if it was going to be the only shelf
This will be the most time consuming step.
Use a contour gauge, make a pattern out of cardboard, and cut each shelf to hug the rounded part with a jigsaw or coping saw. A rasp may be handy for fine adjustments. Be prepared to spend some time and possibly waste some material.
Err towards removing less material and you'll be less likely to have to scrap it and start over. Remember that a 5-6mm gap will be fine, you're not machining an engine block, you don't need thousandths of an inch precision.
Look forward to the steps where these shelves are cut to fit - don't waste time fussing with a good fit in the portion that's going to wind up cut off.
Lay the shelves in place and mark intersection points
This step is easy but it's the key to the layout. Lay the North and South shelves in place on the brackets, then lay the East and West shelves on top of them. Mark the inside intersection points in each corner, on both shelves.
Cut the East and West shelves
The exact angle isn't important, you don't have to bisect the angle perfectly as long as you start the cut from the intersection point. That will be the key to making these fit nicely.
Mark and cut the North and South Shelves
Now you're coasting... put the East and West shelves back on top of the North and South shelves and mark the cut lines.
Check the fit, and fasten the shelves to the brackets, and you're ready to put tracks on it.
Best Answer
I think the answer would really depend on the flexibility of the bar top. You could test the flexion of the board with a jig, and if it's up to muster, then the only other concern is the back corner. That is where the force on the outer corner is going to transfer to, in an upward manner. You mentioned that the angle iron is going into 2"x6"s, so those should be fine.
If the grain of the butcher board runs lengthways, I would stick with the threaded rod, but if it runs the short way, you might run into compression/differential problems with the glue joints.
It's a very smooth idea, I hop you can make it work!