I did see Gael beat me to this, but, you are not going to be able to avoid hacking the servos.
Gael has done an incredible job of designing gear boxes and pistons that take multiple rotations to create a linear output.
Please not that a gearbox as designed here will reduce the output speed and give an increase is the output torque at the same time.
This reduction in speed also reduces the output angle, so if your servo turn 180 degree, then your output will be reduced to a point much less than that.
This means to get the amount of rotation we need the servo is going to have to turn multiple times.
Even with the use of the gearbox to give much greater torque, some of the joints still need a lot of torque, such as the shoulder. While some people have used the smaller servos here, don't expect the arm to lift anything more than its own arm.
The output from the Arduino is a pulse of a set width where the width represents the position the servo is to be in, the servo uses the pot inside the servo to determine what the current position is and drives the motor forward or backwards to reach that position. A pot as used in all positioning servos, has a limited range, typically 270 degree, however there has recently been one that goes as much as 300 degrees.
The continuous type or 360 degree servos, don't have an installed pot, instead they have a resistor bridge with 2 match resistors to form a center point and the PID loop internally is a little altered as well.
If you were to use a 360 servo, then you will have to modify the servo, removing the two resistors, if you can find them and replace them with the wires to your new pot.
It is easier to modify the normal positioning servos, as you just follow the wire from the pot, you are just extending these wires as you are better off using the pot that come with the servo.
Gael has done a great job of showing how to do this on his web site.
I would avoid using the MG996R servo, they are a low powered motor with poorly designed electronics.
How you didn't get smoke out has me beat.
They are a cheap servo, but after you have replaced them a few time, you will find that it would have been cheaper to have just used a servo at 2 or 4 times the cost.
I like the JX PDI6221MG servos, they are stronger, do not suffer the power up jerk the MG996R do and so far I haven't burnt any out.
Building the Inmoov robot will make you learn new skills, learning is not a bad thing.
By the time you are finished, you will have played with 3D printing, electronics, wiring, and programming.
Have a good read over the whole of the Inmoov.fr site, particularly the build yours section even down to the comments.
Gael has put a lot of very good well explained information there.
Regards,
Ray