Thank you for the additional information.
We generally do not recommend putting batteries in parallel unless you really know what you are doing.
From a brief internet search, it looks like those HS-645MG high-torque servos can draw upwards of 2.5A each, which is relatively high for those Alkaline batteries. There are several ways to address this, but you might try switching to rechargable NiMH AA batteries first, which can typically handle higher current draw.
Your idea to use a larger battery pack could work, but as you mentioned, you would need to be careful not to exceed the voltage rating of your servos (or the Maestro). If you use a larger battery pack, you would probably also want to use a step-down voltage regulator, such as the D36V50F6, to keep the voltage at an appropriate level.
Another option you might consider is switching to a 2S LiPo battery, which are often used in hobby projects for their compact size and ability to deliver much more current than Alkaline or NiMH.
Alternatively, if you do not need the setup to be portable, you might consider using a wall power adapter, such as this 5V, 5A one.
There is also the option of powering the system from multiple power supplies to reduce the current draw on each one. Aside from powering the Maestro separately from the servos (which you can find information about in the “Powering the Maestro” section of the user’s guide), you can also separate the servo power rail on the 12-channel Maestro into two smaller power banks by cutting a trance on the underside of the board. This post has additional information about doing that.
Brandon