Is it possible to change the game files so that certain secret projects can actually be built by each faction, rather than only the first one to complete it?

I doubt that this is possible - at least not by just modifying the accessible text files. The concept of "National Wonders" was introduced with CivIII - so adding it to SMAC would probably require real code modifications.

Ah well, couldn't hurt to ask. The concept does exist in-game, though, at least seemingly - for example, you can only have one HQ, but I guess that's hardcoded.

This might not be impossible, you can only make one headquarters.