jaywonder wrote:I pretty much feel that GT either doesn't exist, or it was a version of an alternate universe, similar to the Tenchi series

You're probably not too far off the mark. The presence of movie characters and full-bodied villains in Hell (which completely contradicts Toriyama's description of the wicked after they die) indicates that GT, the movies, and all contradictory filler take place in an alternate universe that bears some similarity to the universe of the manga and the straight-adaptation portions of the anime. Let's call the manga's world Earth-A and GT's world Earth-B. For example:
In Earth-A:
-Kami-sama created the seven Dragon Balls, and the public is largely unaware of them outside of legend.
-Android 8 was created by Dr. Gero alone and failed in his evil purposes.
-When an evil person dies, their soul is cleansed before being sent to Hell.
-The gang first meets Gohan just prior to Raditz's arrival.
-Raditz believes that a meteor destroyed planet Vegeta, and the subject is never brought up while Goku is with Kaiô-sama.
-Scargo is killed by Freeza.
-Gohan never meets Icarus.
-Goku can control his Super Saiyan form by the time he reaches Earth after Freeza's death.
-In an alternate future, Trunks becomes a Super Saiyan before Gohan's death.
-Trunks from the main timeline never receives a sword.
-There are no known adventures of Goku and the gang after he leaves with Oob.
In Earth-B:
-Through various contrivances, all of the Z movies occur (I REALLY don't feel like justifying all of them). Hence, the gang at least knows of Gohan before Raditz's arrival, Gohan meets Icarus, Goku can't control his Super Saiyan form after returning to Earth, and Trunks receives a sword that he will use in GT.
-The child of Katatz created the Black Star Dragon Balls and subsequently hid them in his palace.
-After the split, Kami-sama created a single Dragon Ball and revealed it to the nations of the Earth. They began to war over it, so he smashed it into seven pieces and scattered them over the Earth.
-Android 8 was a collaborative project between Dr. Gero and Dr. Flappe. Gero, having failed in his previous 7 projects and wanting a second opinion, provided a base on which Flappe improved. Since he laid the groundwork for the project, he still claimed it as his, even though Flappe put the real effort into it.
-When an evil person dies, they sometimes keep their body through some unknown criteria (perhaps they are too evil to cleanse, or perhaps they are too strong to be contained in the washing machine).
-Raditz seriously suspects that Freeza is behind planet Vegeta's destruction, but does not voice it to Goku because it would decrease his odds of joining and because Freeza might be monitoring his scouter. Kaiô-sama lies about the planet's destruction so Goku won't get it into his head to try and fight Freeza.
-Scargo is killed by Dodoria.
-In an alternate future, Trunks becomes a Super Saiyan as a result of Gohan's death.
-Five years after Goku leaves with Oob, the events of GT take place.
I obviously haven't covered all the bases (especially with the movies), but that's how it should break down.
To a strong man, the end justifies the means. To a stronger man, the means justify the end.