Personally I couldn't entertain being in a relationship with a known "player", as you said, there would always be a doubt in my mind. Especially given that its recent - 6 months ago, going into their 40's, not exactly old history.
But, perhaps naively, I don't believe people NEVER change, that sometimes people do go from person to person, and then settle down; or cheat and never again.
For me, I'd be asking - what's suddenly changed that means the player life is no longer for her - is it you? I don't want to say you're not amazing, but how many others in the past has she declared they are "the one she'll pack it in for"? Or has another event happened?
Has she actually stopped....or is it just a lull in her busy dating schedule?
How far has she got in the other relationships? Perhaps a clumsy way of saying it, if you reach a previously un-obtained milestone, perhaps she really has changed. But likewise, try and imagine what point you'll have to reach before you could really trust she's genuine - if this point is never, then I wouldn't but if its a rough period of time, or milestone, perhaps. I wouldn't share this though.
Even if you feel you could come to trust her, could you manage your distrust in the meantime? I couldn't not trust, and would hate waiting every time I knew they were at a party, event or whatever, to see if they did/didn't bring someone home. Breathing a sigh of relief if I didn't hear they had, but also worrying...did they and now I won't find out for weeks.
Give it a shot or not. If you do, she could be completely committed, but the doubt will eat away at you and your relationship. Or she'll cheat, But the betrayal and hurt won't be any less just because you knew her history. If anything, it'll add to it in the "I can't believe I trusted her lies!". Or she'll be committed, trust will grow and you'll both have a wonderful relationship.