Just as AnnieBrooke stated, just go by between 3-5 and say "hello." If he is not there to say "hello" to and then he lies about his whereabouts, then react. Is he doing this everyday or sometimes?
I can't comment on his duties and obligations at work. He could have more duties and obligations now than he did 2 years ago thus creating more paperwork. There may be other employees there, but that doesn't necessarily mean they CAN finish his work for him. Perhaps he is staying just to get his job done even though he isn't being paid just because he must complete all his work in order to KEEP his job.
In regards to your comment......"I can't trust him if I ask if he's cheated because he's successfully lied to me before about a girl he slept with before me." Well.....ok, he lied about someone he was with before he met you. Why he would do that, who knows. I wouldn't hang onto that because it happened before you two were together. Perhaps he lied to spare you feelings. Besides this, have you ever had other trust issues with him?
How long have you all been together? Do you all live together?
I am not sure if this is your insecurities getting the best of you or him trying to pull a "fast one."
I agree with AnnieBrooke and would like to add: WhenYou ask Someone a question and they respond in anger it's usually a clue that something is amiss. Asking why He works so many extra hours unpaid is a reasonable question. When He reacts in anger and says "perhaps I'll just quit my job" is a way of getting You to back off, drop the subject. Highly suspicious reaction. Simple questions only require simple answers and shouldn't cause anger - unless there's something to hide??
You want to know what he is doing between 3 and 5, go by his workplace to say hello. You ask "should I continue living with a workaholic," but it sounds like you're really asking "should I continue to put a sack over my head in case he is lying again?" I think if you want to know what is going on, it would not be that hard to find out. Are you saying you don't want to know if he's seeing someone else because you might learn that he is? Where does *that* take you?