well it already got sped up a lot with weekly missions in 2.0 and there is not really anything you can other than do your dailys and weeklies. i mean you can save up your stamina pots for monday sweeps but with the monthly event there is a better time to use them

Join Kyuubi event + Wanted Mission :)

There's ways to optimise EXP for your main:
1) Keep all stamina pots throughout the week and use them on Monday to sweep instances for the double EXP.
2) Do Wanted missions in a team instead of individual for double EXP.
3) Do recommended TI for additional EXP (though I rather you do the highest you can due to better Ninja Tool rewards).

Other than that, its pretty much doing what you're already doing (i.e. Daily, Weekly tasks). For your other characters besides the Main, you can go battle random ninjas around the world map for a pathetic amount of EXP for them, but your Main will not get any.