I was being stupid - its very easy to do this.
Make a column of the custom properties you want to input into the Custom Properties table. Select the section of the column you want to copy and ctrl+c. Open up the Custom Properties table in SW. Delete any preexisting custom properties. Select the only existing row (in the left-most column, place the cursor over the first cell marked "1" so that an arrow like → appears and click).
Clicking should make it look like:
Now, ctrl+v. The column should be copied from the Excel spreadsheet.
Click another cell in the Custom Properties table so you don't accidentally exit and lose what you just changed. Click "OK" to exit. Upon reentering the table, all of the new custom properties should still be there, as copied from the Excel column. You might have to scroll on the horizontal scroll bar to see your new entries if they get pushed outside of the scope of the table window during the copy process.
I realize this isn't super useful if you have templates set up already. However, if you are setting up templates and need to be able to easily iterate on your custom properties list or what order the custom properties are in, this could be helpful. For instance, if you are constantly adding/taking away custom properties for making different templates, it is much easier to do that in Excel and then alphabetize them, then copy them in.