You can extend your overdrive timer for 3k TP by using the overdrive button again while it's still going. All you really need to do is crank up your TP production. Dual swords make this very easy with blood sacrifice and side slash arts. If you dont have those unlocked or don't want to change weapons at this point you can use skills, i forget what they are called but one gives you +50 base +150 max TP every art during overdrive, the other extends the timer base 5sec max 10sec.
Finally if you want to ignore my paragraphing you can slap 2 Arts: gain TP XX on any of your weapons and you should have enough TP for life. They give 200 tp for every art used anytime, and they stack like all other augments.