It is rare you will find any official service department contact for any major company who will work on DIY solutions with you. Even if this was a repair you could probably do yourself they are highly unlikely to tell you how. Financial considerations aside, if they did and you messed up the repair you would be on here saying an offical Apple repair person gave you official instructions and they ended up destroying your phone and what was Apple going to do about it? No way.... We're probably even limited in what we can tell you here since this is, after all, Apple's own "backyard". Certainly if you were asking how to jailbreak your phone that would be clamped down pretty quickly, but I think the main reason given for that is we would be telling you something that would void your warranty and I don't see how instructions on repairing a screen would be any different in that regard. For something 5 years old or more things are a bit more flexible since an Apple Service Center won't have anybody who even remembers those things (gosh, the time I went in looking for a fan for a 7 year old computer and the guy said he had never worked on that model).
If all you do is contact Apple by phone of course they are going to play it safe and tell you to bring it in for study or flat out repair/replacement. They can't tell exactly what is wrong with it by a phone conversation. It's hard enough on the forum here with people saying, "My computer won't start," and it could be anything from corrupt system files to fried motherboard to the thing needing to be plugged into the wall. You've tried the available software solution, so that leaves hardware. As mentioned above, if you're still wanting a DIY solution then you probably need to look on another web site.
