No no no - go the opposite way. You travel back in time to the old west. The game starts as a Red Dead Redemption style game, you've got wild west weapons, you can ride horses, etc. As the missions progress, the Saints of the current time send more and more traditional Saints Row type items back to you - you get modern weaponry, cars (so to start with you own the only car in the whole game), and eventually all the crazier stuff you get later in SR3. Meanwhile, your character becomes more adept at the 'old west' style, too. He can ride other animals, etc, etc.
Then, as the game runs into its final act, there is an error with the time travel and items from all time periods get sent to the Old West - stuff from the distant future ranging through to stuff from the distant past. The final mission? You, and your old west homies, riding dinosaurs in a battle against futuristic giant mechs.
You can give me every single award ever now.