I ended up finding an answer.
SharePoint would not let me filter on fields that were converted in this way, so I had to upload the data already in the correct format. The CSV feed was giving me a string in the "yyyyMMdd" format, but SharePoint needs hyphens between the format blocks like: "yyyy-MM-dd". The FieldRef node inside your batch element also needs to look like this:
"<Field Name='Date_x0020_Field' Type='DateTime' Format='DateOnly'>" + date + "</Field>"
I ended up converting to a DateTime object and then back to string, because I was integrating some other data already in a datetime format, but you could just as easily insert the hyphens manually.
You can convert a string to DateTime with Convert.ToDateTime(stringDate);
and you can convert to the proper format from that using dateTimeObject.ToString("yyyy-MM-dd");