Agreed, get one leg to work first (they all have to move in the same way anyway).
Relays would not be my choice for control but as all is quite slow they probably will do. You're going to need your encoders to know how much your legs really move, the limit switches to find a "home" position from where you can use your encoders to get the leg into position (starting with straight, which will be roughly halfway the rotation).
The more I think of the relays the worse they seem. You need four relays per leg (H-bridge configuration) as you need to move the motors both ways. You can only switch a motor on and off, there is no speed control, and with the weight of your big legs you will have a problem of overshoot.
Another problem, come to think of it, is that your motors will NOT hold position at all. Servos and steppers do hold position. So the moment you switch off the motor as motion is complete, your robot will drop down to the floor again. So... replace your drill motors with servos. That also allows you to get rid of the relays, and simplify overall control big time, including the programming. You can control the speed of servos, you know always at what position they are, and they will hold position for you.
Now the batteries. Get more of them. The problem of servos under load is that they use quite some power to hold their position, so you need to provide a lot of power constantly.
Conclusion:
- get servos (do calculate how much torque the joints will need, you probably need servos that are rated at least twice that to have a comfortable margin and help prevent them from overheating).
- get more batteries (so you can supply the stall current of all servos together for at least twice as long as you intend to use the thing for - you'll be shocked at how much battery capacity you need).
Starting small scale is also a very good idea. Those powerful servos and batteries are VERY expensive.