He's definitely lying. I knew it the second I read your statement about him deleting all the texts before handing you the phone. There's no doubt these two were acting inappropriately before the actual night the physical part happened. I know he'd love for you to believe that the two never even noticed each other and never had any secret contact leading up to their "ONS," but it's highly doubtful.
So is his fake 'work phone' one of those pay as you go phones (called a 'burn' phone) or is it a 2nd line on the OW's cell phone plan that she got for him so they could be in contact without him using his own cell phone which would show up on your cell phone bill?
Apparently, he's up to no good for a while if he's managed to have a fake 'work' phone.
Usually when a guy comes home and 'confesses' to a one night stand, on an occasional blue moon, that's what it really was. But for most, there's a reason they confessed - and it isn't a guilty conscience. It's more likely that the OW threatened him that she was going to tell you about the affair if he didn't start showing signs of leaving you so they could be together. That's a possibility.
It's also possible she found out she had some kind of STD and he freaked out, knowing he'd have to confess to SOMETHING if you were to suddenly catch it.
It's also highly possible that someone you know saw them together and he freaked out, thinking this person would tell you, so he 'told' you first.
Another possibility is that someone told him they didn't like what he was doing and if HE didn't confess to his wife in the next few days, this person was going to do it.
Whatever the reason, he was suddenly motivated to 'confess.' But of course, as ALL cheaters do, he lied and minimized and watered down the story to a 'one night stand.' That's what they do - confess to the BARE minimum. People having accidental one night stands DON'T have fake work phones and they DON'T erase all their texts before giving you their phone.
He had lots of time to clean out all his email accounts long before you logged in to look at them, so those are a lost cause at this point.
I think your MC's advice about time away is stupid, to be frank. Instead of suggesting you get away, maybe the MC should concentrate on getting your lying husband to start telling the truth so you wouldn't HAVE to go away because his lies are driving you crazy.
I'd seriously consider strapping him into a polygraph chair. After all, since he insists that he's told you everything, he should have NO problem taking a polygraph test. In fact, one would think he'd JUMP at the chance to prove to you that he's being honest and to finally shut you up with all your accusations - right?
Don't hold your breath. The guy is lying through his teeth.