I usually cut another hole besides the oblong one in my commercially built inner covers....70mm or 2-3/4" hole (wobble the hole saw around a bit to make a nice fit for the jar lid). But...I usually put the screen on the top side (#8) and simple stand the jars on top. I can feed 1/2 gallon at a time with the two holes.
I like the holes being screened because I can replace the jars without having to shake bees off the jar lid or having them fly up out of the holes. When all that I'm doing is simply replacing jars of syrup I don't wear a veil.
What iddee said about ants building nests between the lids gives me food for thought, though. I've got a friend that has had problems with ants doing this and he uses screening over the holes in his inner cover, too.
The feeder that Moots is showing would probably be the answer to the screening/ant issues. I would think that you could permanently add some screening and use it as long as you are feeding. If you only use one jar then drop a *solid* lid in the hole to keep the bees from propolising the screen. Once you are through feeding for the season then remove it and give the bees free access. Using the feeder that Moots showed you wouldn't have to pull staples out of the inner cover to open it back up. Naturally, without the screen on the inner cover you will have bees fly up all along when you remove the telescoping cover. These feeders seem simple enough to build...even I could probably one! Kelley sells them but $14 a pop seems a little much for them. :?
As for the answer to the mat299, the bees will get the syrup through the screening. One-piece lids are the best as they don't recess inward. Using regular canning jar lids might cause the bees some problem in that the lid part is recessed toward the jar creating a small distance between the surface of the screen and the lid surface. I had an older beek to tell me to simply flip the lid over in the ring so that the gasket faces outward...this also reverses the "recess" of the lid and makes it protrude outward toward the bees. He said that it would not leak but I have not tried this, yet. But, if the surface of a lid is in contact with the screen then the bees have no problem getting the syrup.
On another note, I see you're over in Georgia so SHB are an issue for you. Beetles will enter the hive through the holes in the inner cover and will readily pass through #8 screen. I tried some regular window screening last year and noted a higher number of beetles scurrying around on top of the inner cover (to be little greasy bug spots shortly thereafter). The bees could still take the syrup through the screen (close contact with one-piece lids). But, most of the time that the window screening was in later summer when I wasn't feeding very much. Eventually the bees propolised the window screen closed....had I covered the screen to block the air movement or light(?) I think the bees would have left it open. The window screen did reduce the access points for the beetles but no matter what you do the beetles will get inside the hive so beetle traps are still a must. I'm a newbee, so take what I say with a grain of salt. :)