Your options appear to be:

  • Marry before she goes out of status, and seek to adjust status on the basis of marriage;
  • Marry after she goes out of status, and seek to adjust status on the basis of marriage;
  • Marry before she leaves the country, have her return to her country, then seek a spouse visa;
  • Marry after she leaves the country then seek a spouse visa; or
  • After she leaves the country, petition for a fiancée visa for her return.

The riskiest prospect is to have her overstay before you marry, as if immigration authorities pick her up she's likely to be put into deportation proceedings. But as she entered lawfully on her J1, her overstay (whether pre-petition or post-petition) would not prevent her from seeking to adjust status on the basis of marriage. The safest approaches are the ones that keep her status lawful at all times, but given the dates you describe they also require a period of separation. As I'm sure you know, when she's out of status she should not be working.