A few thoughts.
1) Your water is not hot enough. Almost all cooking greases with melt at 120F. Water temp below this and the grease will remain adhered to the item being washed. All three compartments should be maintained at 120F or more, especially your rinse compartment.
2) Soap to water ratio too low. You should have a HUGE pile of soap bubbles in your water. If you find it hard to easily rinse off all of the soap, then you have enough. If it rinses off really quick and easy, you don't have enough soap in there.
3) Change your water frequently. Our general rule is to replace water after three sink loads. (recycle all three compartments)
4) Ensure that your sink interior surfaces (all three compartments are clean and clear of oil/grease). It doesn't take much accumulation on the inside surfaces to coat your "clean" utensils, etc. We scrub all three compartments with hot water and soap between each time we cycle our wash setup.
5) If you are using bleach in your sanitizing compartment be aware that high levels of bleach will leave a "greasy feel" to surfaces. Minimum 50 ppm, maximum 100ppm, we still use bleach as sanitizer although Quaternary Ammonium is the preferred sanitizer now. Some still use bleach b/c of lower cost and the limitations of Quat's effectiveness under certain circumstances.
We had a similar issue early on in our business and increasing amt of soap, changing out water frequently with a good wash down of the interiors and using test strips to ensure the correct amount of bleach was being used solved it for us.
p.s. Quat is know to leave a "barrier film" on surfaces.
p.p.s.s. Try adding vinegar to your rinse water to help ensure that no film transfers to your sanitizer compartment.
