I got a number of feedbacks on my question what Kennedy Space Center considers as a large bag. They look promising. However, no official word from KSC yet (but, granted, it was weekend and now is nighttime in KSC local time, so it’s not the time to be impatient).
I’d like to thank all of those who commented. And if you have any thoughts on the issue, I sill appreciate any feedback. I’d like to quote two comments which probably make a good summary:
One is from the nasaspaceflight forums. Thanks to mceddiemac for it:
I think you will be OK with those. Last two times I was down there (STS-116 & STS-117) they allowed me (and others) to bring in medium size backpacks. Mine had all my camera equipment in it and measured 18″ x 12″ x 8″ (45cm x 30cm x 8cm). They also allow the compact folding umbrella chairs that are carried in shoulder bags. Security will check the contents of the bag before entering the Visitors Complex and will let you know if its too big and probably allow you to put them back in your car if thats the case. Like I said, I think you’ll be OK.
The other one is from Cloudy Nights, thanks to mattbtn for it:
I think you’ll find that NASA is far more restrictive on their website than they are in person once you get to KSC. I was easily able to get in with a large camera bag, which is about as large as your sling bag, and my wife carried her purse. They understand people want to carry large camera equipment, folding chairs, etc…so as long as you aren’t bringing something just truly obnoxious I think you’ll be ok.
In summary, it looks like my bags are OK. I will now pack them. I will also be at KSC the day before launch, and I’ll check with security as a late measure. Maybe they even allow my small backpack in… But anyways, I don’t want to ask too much. I am happy if I can get along with the mentioned bags ;)