There are 2 generic approaches to this requirement. There may also be something specific related to the report layout and how you might trap the data only in the section you need but that's difficult to assess without seeing the report.
The 2 generic approaches are:
1. Look for specific data characteristics in fields in the detail template that only occur in the sections you want to include.
My impression here is that this may not be possible with your report since it successfully pulls everything including "today" but there may be something you could use that would skip today's records. It might be in field or, possibly though rare, something that appears in front of the data in the row. See the Advanced Properties, "preceding string" options. In certain circumstances that might offer a way to include or exclude entire records no matter that the Template would try to pick them.
2. Take the entire report, Today and the sections you want, and filter out the records for today leaving only older data.
This is probably the best way forward or you since it most likely just means adding a filter and a field that can use it to include with each record.
So if your Report Section header has, for example, the text "Report - Month End" you can trap that as an Append Template or perhaps in a Page Header template and that will add the field to each record in the data table. It is likely that the same field position in the "Today" section of the report will show "Report - Today".
If you then filter the records in the table using that field and have Monarch select only the "Report - Month End" records you will have what you need. You can hide the field that you are using for the filter if you wish - the filter will still work.
This is a very basic description - there are some much more powerful and elegant ways to do things like this should they be required. But for a simple extraction selection you may as well keep it simple and easy to follow since the result would be the same!
Normally I would go with the filter solution.
The only time a selection based solution might be appealing would be if the number of records extracted for the table simply had to be reduced compared to the overall report size. In other words a very large report that exceeded system capacities and for which many many unrequired records were likely to be extracted. Clearly that is not the case for the report you describe so extract and then filter is the most obvious and most flexible solution.
I hope that helps.