Sears has good batteries. Some say Optima is good too. I think for my accord exv6 I bought 100Amp die hard gold.

Change the battery and then see what problems still exist. You might be just at the margin voltage and exceed the margin when your RPM is higher.

In regard to diconnecting batteries. ALWAYS dissconnect the positive side.
Why?
Because the negative side connects to the chassis in many places. If you disconnect the negative side you will still have Floating Voltage with your positive being connected but you have no ground, just parasitic ground. With the ground being absent, you never know what that voltage would be.