Before you reach back out to your ex and try to bargain to take you back and tell them that you'll do this, and you'll change that about yourself. It doesn't matter that you're not getting married, it doesn't matter that they don't want a serious commitment.
Think about it really quickly. Are you doing this simply to get your way or are you doing this because you really feel that those things aren't important to you? When you start to bargain, you start to diminish your value and your sense of self-worth.
You wouldn't go back into a place of employment and say, ‘hey I'll take five dollars an hour instead of 25 an hour’, because even if they agree and hire you back, or they take you back as an ex, it's only a matter of time before you start to feel that resentment or the bad deal, the bad shake that you got out of the deal.