I actually got the whole screen to work, after pushing on the back/front of the brown ribbon AS WELL as the connection point on the actual screen with a combination of the iron, a pencil tip, and a pencil eraser. It was EXTREMELY stubborn, I burned my finger something awful, and the entire process probably took around 4-5 hours but I couldn't be happier :'D

You really want to use a dab of solder to even the heat on the ribbon cable. I've found this to help a lot. You will want to put something over the LCD though so nothing spatters and melts the polarizer on the front.
But sometimes the glue is just so dried up it won't remelt and reattach and if you heat it up for too long you will actually bake the glue and then there's nothing you can do.

Sometimes, the lines won't go away no matter what.  Try this: if you have a heat gun, make some kind of small nozzle for the air to go through, maybe using aluminum foil wrapped into a funnel???  Try to focus the hot air into a small area, that way you can concentrate on the area that needs to be worked on.  Also, work on that cable up right by the screen, & down away from the screen as well, moving back & forth.  You may get lucky.  I've found hot air to do this much better than a soldering iron.

its happened to me...

To answer your question: Not long. I got it down to 2 lines now, but they're quite stubborn! D:< One of the things i found useful was pushing with the eraser side of a pencil on the flatwire, as well as pushing from the back of the lcd-flatwire meet point.

How long were you messing with it by trying to heat the cable?

I've done this three times and managed to get all of the lines back every time, but it can take a long time… I think it took up to half an hour straight for some of my front PCBs. I've recovered screens that were half-gone before.

If you use the right heat, keep the iron moving, and make sure to keep your iron tip coated in a fresh tin (both for efficient heat transfer and for the sake of not ruining the tip), I think there's a good chance you'll be able to get the back with enough elbow grease.

sometimes lines are just broken... maybe somewhere in the brown flatcable.

if the soldering iron or heatgun won't work, maybe you're just out of luck?
Unless someone has some more tips...

So I attempted to repair quite a few lines (10-14ish?) on a DMG using the classic heat gun/soldering iron method, and it seems that every other vertical line in the particular group doesn't want to display, no matter how many times I try to heat it. I tried removing the screws that connect the brown cable to the actual gameboy, and this helped a little... Any thoughts?