I'm not sure about the conflicting advice because I wasn't one of the ones who offered advice, but I've been following your thread and one question I have is 'what's the rush?' Another question is, 'what if starting over as friends is the path to reconciliation and a full relationship?'
It seems trust needs to be re-built and things need time to evolve naturally. Perhaps you don't need to arbitrarily ask her out but what if there happens to be an event coming up that touches on something you and she used to enjoy together? Like if you used to attend the annual auto show together, or if you had a special place you'd go together to watch the 4th of July fireworks? What if one of your old mutual friends happens to be coming to town and you think she might like to see that person when you meet up with him or her...
In such case there'd be a reason why you're asking her out and she'd have a reason to say yes outside of simply implying to one another that it's a date to see if you can rekindle the romantic interest.
I guess I always look for the middle road but perhaps others will continue to tell you to go one way or the other and it's up to you to decide!