How can I predict the spread/span of a single IR beam?
You have the 'spread' of the beam coming out of the IR diode. You will find that from the angle diagram of the IR diode. 

Here is a diagram of an IR diode specified as 120 degrees:


A receiver also has a 'viewing angle'. You have to see if the shadow of the object is well withing the viewing angle. That is more physics (although very simple physics). 


Simplest way to improve coverage area is to use more then one detector. Because they conduct when light falls on them you can put them in series.

Very important is to make sure no other IR objects are radiating into your sensor. (e.g. the sun) 



Post edit:
Of course you can do what they show in the movies: have a series of mirrors bouncing the beam back and forth from top to bottom.

(Make sure to leave a big gap at the bottom for the hero to crawl through.)