Steve, I am sorry you are going through this issue. It is tough and you are not alone. This is an all too common occurrence today. To be honest, there are not many avenues for you here. That said, there is one avenue you can take that will allow you to take the legal advantage and get more time to remove personal belongings. That avenue, though, will require you to petition the court in which the divorce is pending.
If I were you or your lawyer, I would file a motion for an extension of time relative to removal of your belongings. Here is the trick, in the motion, you can state that your wife is attempting to leverage the short turn around for removal of property in a move to make you assume debt. The motion should be granted by the court because it is unreasonable to sift through that much material in such a short amount of time. In mentioning what is going on in the motion, you hope to gain a legal advantage with the judge as well.
This is not easy and I know that filing with your lawyer can be expensive. However, it should be much less expensive than assuming that much debt.
Let me know if you have any other questions or comments. Please also rate my answer positively (THREE OR MORE STARS) on the ratings bar on your end so I can receive credit for my response from the site.
Thank you and best wishes!