Also running 11880's from ImagePrint, here. Printing from IP or Photoshop will have no effect on head strikes. What else can you say about the case where this is happening? What type of paper, what's your platen gap set for, what media type is selected, are the strikes happening on the edges of the paper or in the centre somewhere, is it happening in areas of heavy or light ink loads, etc.?
Also, is it really head strikes, or is it ink droplets? Or ink on rollers being transferred onto the paper? You description kind of fits all three possible scenarios.
While diagnosing this, stop power cleaning. That can be destructive to the head, and if it's not solving the issue it's a risk not worth running.
I will surmise that if you've been running this printer for 4 years with a moderate to heavy work load, you probably could benefit from replacing the whole cleaning/capping unit. (Unlike the x900's I don't think the 11880 wiper blades would be easy to replace by themselves.) Release the print head, slide it out of the way, and shine a flashlight in where the wiper blades & capping station are. Do you see a ton of juicy ink, dust, fibres, crud and whatever else in there? Or does it look pretty clean? Crapped out cleaning & capping stations I firmly believe is a huge reason people have trouble with Epson large format printers.