Never have to start a new game in ootp14 to use graphics in the 2013 all-in-one mod. For logos, just go to your saved game's news\html\images\league and team logos folder and delete everything that doesn't start with default. Restart and you'll have all the new and your old if it wasn't in the mod.
You can pretty much do this for any of the graphics that are saved in your saved_games game folders. Unis, logos, photos, etc.
If you are using/want to use the ballpark pics in the same mod, go to any teams edit ballpark page, click the import button and select auto import all ballparks, navigate to your ballparks folder and click select and all MLB ballparks and data will auto import...no need to create a new game for this either.
Acutually if you get Gambos ballparks mod from ootpmods.com, he has now created .prk files for those. Now you can use those same steps and auto install those as well.
As for best time to import your ootp13 lg. Here's what Markus says. "Import anytime you want during the game year."