I used to have this same problem, but not any more. I came up with the perfect method of cleaning the LCD panel. First of all, I had no idea that alcohol would damage the LCD. I normally use 90% Isopropyl Alcohol for cleaning everything on the smartphones and tablets that I repair. I might change that back to a pre-mixed 50% solution, but the 50% does not remove grease as well. I honestly don't think a 1-time cleaning using the 90% will cause a problem. I could believe that continued cleaning with the alcohol could cause damage, however.
What works best for me is to follow this 3-step procedure. And take note, scrubbing an LCD with a back-and-forth motion will only get you frustrated, just as the previous poster had mentioned. I've been there, rubbing on an LCD for upwards of an hour, only ending with the same grease smudges that I started with. Well anyway, here's my 3-step process:
1. Using a micro fiber or dust-free cloth, or even a soft toilet paper, put a liberal amount of the alcohol on your cleaning cloth and use "flood-strokes" on the LCD in one direction ONLY. Wipe down the LCD in as few strokes as possible, as wide of a stroke as you can with your cleaning cloth or TP. You should use enough alcohol that it leaves a wet film on the LCD.
2. Blow dry (with your mouth or a heat gun on low) the alcohol. It will disappear very quickly. If you see any spots, repeat step 1, and then do this again. You will see residue on the screen, but it should be very uniform, and in the direction that your flood strokes were in step 1. If you do this right, you may not see any streaks at all.
3. Using your hot breath (hopefully your breath isn't so bad that you melt the LCD, so be careful here), steam up the surface of the LCD and use the lint-free cloth to wipe the steam. This will get rid of all the residue left behind by the alcohol. It's okay to wipe in a back-and-forth motion when using the hot-steamy-breath application of moisture. In only 5 minutes, your LCD should be completely free of streaks, grease, and dirt. Blow away any excess lint, and get the glass digitizer put on it as quickly as you can before your LCD attracts dust out of the air.
One thing I would also recommend is that you have a good filter in your HVAC system. Some people I know of actually use a hood that forces air through a filter, and into the hood. This way, you don't have any ambient air coming into contact with your LCD, because you are operating in a positive-pressure environment with incoming air that is filtered, and thus exhausting into the room after leaving the hood.
I will be writing a post on this and possibly doing a video for my blog site, which is the Carlton Zone Blog. Check the site soon. I would be glad to post videos and advice for repairs, because I do a lot of this.
Hope this helps, and let me know if it works for you!