I think you have identified many areas that need to be addresses. There are literally hundreds of variable that effect output from customer to press sheet. I think something you should address first is the ink. If you can visually see a difference in the ink from batch to batch, then that leads me to wonder if the milling changes, which can effect particle size and suspension.
If you have a local INX dealer, give them a call. I have used INX ink for many years, and have neve had any issues. They are generally very knowledgable, and can suggest a good fountain solution for your press as well to match the ink and plates you are using. That would take care of the ink triangle: ink, water, plate. This would include cleaning the recirculation system as well.
Next, consider a very thorough cleaning, using paste on the rollers, pumice if necessary. Make sure to get into the bottom form rollers. If you can, have the pressman pull out the entire roller train, ink and water (carefully of course), and clean them off press first, then put them back on press and clean again. While they are out, clean any area of the press that can be reached.
Third thing I would suggest is a new set of blankets.
The temperature, humidity, air quality, and air flow in the predation are also something to consider, although they can be mitigated if the press is kept in tip top shape.
Sometimes I think managers and owners that have never been press operators really don't understand what is going on, so they can't understand how to fix it. I started out at the bottom before I was able to own my own shop, then have employees. I think it gives a better perspective of what's really going on. If my pressman has trouble with something, I can actually understand what he's talking about. I've also been very pro-active in maintenance. My father taught me that, and I think it helps out in printing. Changing blankets, rollers, and pro-active cleaning, even on our 3302 or 360, seems to help keep problems down, and downtime to a minimum.