If they release a larger screen phone it won't be the 5S because it won't have anything in common with the 5. So like you said it will be called something else.
That said I doubt we'll see a larger screen on this release. From what I read the point of the cheap iPhone is too sell to different markets. And to reduce fragmentation.
By adding another screen size they will only be adding to the fragmentation.
I don't think as many people care about screen size as you think. Sure the avid enthusiast on this forum do but that's a pretty small percentage of Apple customers. I'm still happily using my 4S. Would I take a 4.3-4.7 screen? Sure but I'm just fine with 3.5-4.
I'm hoping for a slew of new hardware and software features on the 5S. If a larger screen is one of them then great. If not...meh.
What fragmentation? Apps submitted for iPhone are currently required to have retina elements and iPhone 5 resolution since May. Do still think there are developers who only update their apps for the old iPhone resolution? No. They are requested to have the above by Apple or they will be taken out of the store. In the case of iPad, apps either contain retina elements or they don't...how long before Apple requests that they must have retina too? So there will really only be 2 resolutions to program for. Adding another resolution will not really cause any fragmentation, at least no more than when developers had to include 320 x 480, 640 x 960, 1136 x 640, 1024 x 768 and 2048 x 1536. I guess Apple want only 1136 x 640 and 2048 x 1536 (if they update the Mini to retina) by next year, so a new larger iPhone display will not be too much hassle if devs can drop older model resolutions....i think