The nice thing about my theory, though, is that it allows the reader to focus just on the game timeline (where Mario and Luigi have lived in the Mushroom Kingdom all their lives) and completely ignore the branch off that leads into a timeline loosely based on the cartoons, comics, and movie, if they choose. And really, the most fustered-up part of my theory is just the in-game story of Yoshi's Island DS itself.
In Star Wars canon, the policy used to be that any source that contradicted canon had to be thrown out entirely, but since 2005, they've changed it so that the contradictory parts can be surgically removed, and anything that doesn't contradict higher canon can stay. For example, the N64 podracing game used to be totally non-canonical because it could depict Anakin podracing multiple times leading up to the Boonta Eve Classic, but since the policy change, it can be considered partially canon; the part about Anakin racing before Episode I is thrown out, but all the planets and locations that were created for the game can still be considered to be canonical. I try to take that kind of approach in my Mario canonizing. There's nothing in the games to say there's not a Founder's Day, and it's not completely stupid, so hey why not.
What about all the callbacks that are made to previous games? Granted this happens mostly in spin-offs calling back to previous spin-offs or games in the main series, but it's definitely something. Otherwise I thought the assumption was that the games took place in order of release save for a few special cases (such as Yoshi's Island, or Mario Party 2's plot being a stage show).
Callbacks are rarely explicit, though. Like, a Geno doll shows up in Superstar Saga, but Mario doesn't say, "Hey! I recognize that!" There's very rarely anything like the ties between Zelda games. It's pretty much just Lady Bow in TTYD saying "Oh, hey, remember our last adventure? That was fun!" and a general sense (in more recent games) that Mario has a reputation for rescuing Peach from Bowser. There's a few more ties if you expand out to manual text (SMW's manual explicitly says it takes place after SMB3, and SMB3's manual implies that it takes place after SMB, TLL, or both), but still, it's pretty sparse. They tell us that the games all take place in similar universes, but to say they're all in one universe and are all consecutive in some fashion is a leap on our part.
(Also, there's no way that the Parties and Karts should be placed in the timeline along with all the other games in order of release. It's too big of a shift to have Bowser crashing Mario's party one day and getting punched into the sun by Mario the next. The Mario Party games are stated to take place in "Mario Party World", so let's assume that's some kind of alternate universe separate from the Mushroom World of the main series games, and that the Karts and sports games also take place there.)