In the Databanks in the Upper Left toolbar there is a "The Story So Far..." that tells the history up thru GCII Dread Lords
Technically speaking, the leaders from GCI (at least the human and altarian ones for sure) should be dead by the time the events of GCII happen. GCI starts in 2178 so even a conservative estimate on Alan Bradley would either make him extremely young when he took office, or extremely old now.
In any case, truth be told, they didn't have a lot of money to do GCI, the story was based on Brad's writings from the late 80s, early 90s, and if Brad got the chance, he'd probably go back and re-imagine the start of the series if he could.
Mostly, you just need to move the majority of the events of GCI closer to the events that happened in GCII. (called a mental disconnect)
As compared to the Zelda series...while the Zelda team has stated that they do have an overall timeline, each game occurs, generally, in its own place in that timeline and are not directly sequential of each other. The events of one can be hundreds or thousands of years apart from another. The names and places may be the same, but thats more from Hylian mythology affecting every day life (to quote Battlestar Galactica "all this has happened, and will happen again")
Anyhow, hope this helps a little