OP, totally agree with everyone who says that he must disclose totally now - now, not in the future, not death by a thousand cuts, but now. As already mentioned, if you discover more down the line - and you will, trust me, as you have already found since your initial suspicions -it will mean that any attempts to rebuild your relationship will have been on foundations of sand.
My DH only admitted to his numerous sexual encounters with his OW some weeks after first confirming an 'EA' (after I had been warned by a phone call from a female colleague of his, bless her), and then only because the OW had threatened to tell me about them, some of which took place in my own home, in a bid to put pressure on him to leave me.
It not only put us back to square one, but it made me realise that virtually everything he had said to me thus far had been only about 20% of the truth. He lied and minimised because he suddenly realised that the entire terrible truth may well lead me to end our marriage; ironically he was still besotted with the OW at the time but was beginning to suspect that what he thought he had with her really was just an illusion and therefore he didn't want to burn his bridges. The problem for me, and for him, was that I had almost driven myself mad with the certainty that it HAD been physical and that they had had much more of a relationship and social life together than he was prepared to admit.
The truth when it came was beyond awful but in a sense it was also a relief because I knew, finally, that I wasn't 'paranoid, obsessed with her, unforgiving' in the way I had claimed up until that point.
And it still goes on - only a couple of weeks ago I came across a note from her in an old work jacket of his I was taking to charity which confirmed that my suspicions I had had about their very last meeting, what they did and where it took place, were totally accurate, despite his vehement denials to that day (nearly three years on). The pain was raw when I read it and I was catapulted back to the early, agonising days post-discovery. When I rang him at work to rage about it (yes, I know, I know - but I am impetuous and hot-tempered), he said that he hadn't wanted to tell me because he had lied about it for so long and he felt it would be humiliating for me, and make me doubt him once again. Arrgghh , even after all we have been through, and he has worked so hard to be transparent, he still had to dissemble over that one because to do otherwise would have meant confirming that the OW's claims to me about that day, which he had strenuously denied, were in fact true.
But please do remember that none of us, no one, would want to admit the sort of behaviour indulged in during affairs to one's DW or DH unless you really wanted to ensure it was an 'exit affair' and that maximum hurt would cause maximum effect. Put yourself in his shoes - if it had been YOU, would you want to say, 'yes, the OM put his cock in me and gave me a great orgasm and it was just fantastic and I didn't for one moment feel a shred of guilt about you'? Think of the words of Roberta Flack's song, 'I felt he'd found my love letters, and read each one out loud'. When you are in affair bubble world you deliberately choose to ignore the massive likelihood that it will be discovered, because, hey it's not going to happen to you, is it?
But it was discovered, by your female instincts and now it's like the personal version of a kiss and tell story - totally humiliating because he has to admit to doing truly awful things. It doesn't mean that he shouldn't put his cards on the table, but people stand in court on a daily basis and swear blind they didn't rape or murder someone, even when their DNA is all over the victim.
Believe me, I have not a shred of pity for him, but I know that had it been ME that had had the affair and not my DH, I probably would have minimised the truth from my DH, in order to protect my own skin, save my marriage and not have to admit what a total bitch, tart and thoroughly dishonest person I had been. My DH's OW told her DH everything, pulling no punches, even down to the sexual positions and acts she and my H had performed on each other, in order to maximise his devastation and try and prompt him to throw her out so she could 'legitimately' turn up on our doorstep. When her H and I discussed it some months later he said that although it was like being burned with acid, it hurt so much, in a sense it got all the shit on the table so he knew precisely what he was facing and the fight he had on his hands.
You don't have that clarity, yet, OP, but somehow you have to impress upon him that no matter how humiliating it is, he must tell you everything. If he doesn't then he and she still have secrets between them and that is unacceptable. And yes, yes, yes to not going away to the course and getting another job. In the end my DH leaving his job - he worked with the OW - was the real catalyst to us beginning the long haul to staying together. Thinking of you.