FWIW, you're the only other person I've seen acknowledge that Gateway is an AI novel not an alien archeology novel. The Heechee are just a plot device.
The first novel is different than all of the others because of the psychological intensity and claustrophobia. (e.g. it's a story of a civilization at the breaking point, not after it was broken or facing permanent expansion.)
The other ones are ahead of their time in terms of the idea of "downloading".
The other ones are ahead of their time in terms of the idea of "downloading".