Hummingbirds are not going to be able to feed through window screening. If you do a web search, you will see where they are injured getting caught by their beaks in window and door screens more often than you may have thought.

You may need to change your feeder style. Bees cannot get into Perky Pet Oasis, and it has a built in ant moat. About the only insects you might find in the Perky Pets are drowned gnats.

Im not familiar with type of feeders you speak of. I usually just use the cheaper standard type of feeders. But I have had a terrible time with wasps getting in most feeder holes including hummzingers. But this year with using certain style feeders with some adjustment on portholes on some feeders that were just too big I had little to no bee problems. Once I made the following adjustments wasps still tried for a few days maybe a week but after that they gave up trying .

This first one shown is a first nature 3091 with easy snap on and off flowers for easy cleaning.

the next one is first nature 3051 16oz feeder in which the oval ports were too large and most wasp types could enter - so I got some craft sef-stick cut outs and made the holes just big enough hummer beaks but bees could not get into it. I was well satisfied with the result. When mold would build up I would just soak the bottom half of the base in the sink with bleach solution--- 1 cup in half a sink full water.