I was able to get on the phone with DB and they gave me the same info unfortunately. Just another example of how tedious intra-Europe train travel is. When a strike happens in Germany, DB is usually very generous and converts all tickets into flexible ones that can be used during the following week or so.

The guy told me that since the strike was NS's responsibility, ultimately they would have to be the ones to rebook you onto today's connection. (I realize that NS gave you the exact opposite information.)

As a final resort, try speaking to an customer service agent at the station or the conductor of the IC to Cologne before you board. They might have some leeway in this regard.