Personally I think Heine was in GSD, what Samuel L Jackson was in Star Wars. A cameo by a guy that either wanted to be in the story or was asked to be in the story just for heck of it. He had no real character, they never developed him, nor do I believe did they ever intend to. His attraction? The fact that he was a blank slate with poofy hair an a nice voice. He could be whatever the viewers imagined him to be because he was so "mysterious" and thus embodied endless possibilities. If you put swirly glasses over his face, give him Steve Urkle's voice from Family Matters and made his hair look like a troll doll he'd lose most of his appeal (which is mostly based on physical trait with nothing really to back it up in my mind). Personally his posing for the little time he did have made me kinda yak... but that's just me. If anyone goes back, they can see Heine's gundam in action before he's killed in like eps 1-8 or something. They show this little orange gouf blowing stuff up.
He was the guy that Fuka didn't have to "screw up" which made him that much more popular.

Edit: As for a what Terra has suggested. It sounds aweseome!!! @.@ Send me a copy of the fanfic if you ever decide to write it. My personal ideas as to what Heine would have been if he had not died... The 'Rey' to Athrun's 'Shinn'.