How I saw it
Here is how I saw it working (using Solid Snake as an example). the Solid Snake page would be a disambiguation page that linked to the others. For each game there would be a corresponding character page for instance Solid Snake(MGS1) This would only deal with information from that game. This could be started by taking the current MGS section and making it into an article. On each page would be links to the previous and next pages. Each character would get a category so that the character pages and other relevant pages could be grouped together. (for instance the bandanna page in Solid Snake, Big Boss etc).
This would work in a point of view kind of way. So past events could be briefly referred to if it was relevant to current events. however it would be expected that most of it would be left to the article it belongs to.
Since older games could be mentioned this could lead to "spoilers". I think we should take our cue from the game, if it wasn't necessary to the plot then don't mention it. apart from that I'm not too concerned about spoilers otherwise it gets complicated. Future Events obviously wouldn't be mentioned. If a current fact is contradicted in a future game then the current version would still be mentioned as it would be corrected in the other article
Lets try it
Notable changes to the character could be linked from one character page to another. the infobox would be more relevant containing current affiliations, photo, aliases etc.
having multiple pages probably won't be ideal for every character we have.
two-game characters are probably the most natural fit. Since the changes in the character will be most obvious. Eva for instance is a completely different character by MGS4.