A good way to help line them up is make reference points on the outside of the board (like one on 2 opposite corners), once you have one side, drill tiny holes in them and poke a pin though them, now when you go to put the other side on you can poke though the paper on your reference marks
it wont be perfect, but its better than trying to eyeball it
two other things to keep in mind is that autorouting is pretty dumb, and sometimes just moving something or rotating it will give you what you need
Also, by ordering one alone I think the price will be high, right?
I doubt you will find a house with a minimum order of one, and it adds up real quick