The final benefit of the War Caster feat says (PHB, p. 170):
The spell [...] must target only one creature.
If my character is level 5+, does a spell like eldritch blast still meet this condition as long as all of the beams are directed at a single target?
Basically, does the "must" just restrict what targets I can choose for the spell? Or does it restrict the selection of the spell itself based on what I can target?
Your above quote is actually a slight misquote, but it lead me astray in answering this question. The last line of the third benefit of the War Caster feat actually reads (PHB, p. 170):
The spell must have a casting time of 1 action and must target only that creature.
A casting time of 1 action is a property of the spell and not the casting – so from an initial reading it would appear that the question of how many creatures the spell targets would also be a property of the spell, rather than the casting.
However, the text says "The spell [...] must target only that creature." This means that the spell must target a specific creature as opposed to any single creature. This is not a property of the spell, since it can only be decided at the time of casting – so as long as the spell only targets that specific creature, it shouldn't matter if it has the potential to target more.
With regards to your specific question, as long as you only target the creature which provoked an opportunity attack, Eldritch Blast should be a legal choice for the spell you cast as a reaction (even when you're level 5+).
