To be honest, Starting, although it's a risky gamble, I don't think I could have resisted meeting him either and showing him how over him I was and that the tables had turned - he was now the beggar and not the beggee.
I remember my SIL agreed to meet DH's twat of a brother at his request after he'd been chucked out for having an affair for the second time, with the same OW. He was a liar, too - in her words 'He lied and he lied and he lied.'
I was very apprehensive and thought she should keep him at arm's length - he can't half spin a line. But she had toughened up in the meantime. She had lost loads of weight due to all the upset and replaced her now too-big mumsy clothes with an edgy new wardrobe. She told me when she walked in his jaw dropped, his eyes nearly popped out of his head (not a good look - his eyes are too prominent already) and he gasped, 'My God! You look fantastic!'
She said that moment was really sweet and she relished it. Despite my worries the meeting boosted her morale no end. She left the restaurant walking on air having told him he could do one.
Warning: it didn't stop him turning up at her house unannounced soon after and asking for money to clear the debts he'd run up having foreign holidays with OW!!
I do wonder about your Ex - do you think he's oscillating between you and OW saying sorry (in her case probably for the domestic crime of staining her carpets) with the intention of moving in with whoever caves in first?