This is the glue that I use. It is for Styrene and plastic, works really well and dries pretty quickly which is a great help for projects like this. This comes in two different strengths, for something like Kato track, I like to use the stronger one which melts the plastic a bit more.
And we simply apply it from the bottom, it'll wick through a certain amount, melt the plastic, then dry/cure and you'll have a good weld.
I then put some on the top as well. BUT, I've found that it melts the black ties causing some colour run. As these tracks are going to be glued in place I don't think adding glue to the top is necessary but it sure is strong.
Then the rails need to be cut off:
And after cutting, file off any burrs.