Short answer:

A transformed Beta distribution policy is an option. See for example in this paper. However, I haven’t personally gotten Beta distributions to work. The training is always very unstable.
Have the network output actions in [-1, 1] and transform to the desired range as part of the environment. See here 3.

Long answer regarding the transformation of sampled actions:
In general, doing a location-scale transformation of your clamped actions in [-1, 1] should not affect the SAC entropy correction formula. To see why, consider your transformation of the type l + c*a, where a = tanh(u) just like in the SAC paper (l being a location term, c being a scaling factor).

The term in the log behind the sum comes from the derivate of your tanh transformation. If you instead take the derivative of l + c*tanh(u), the term l will immediately fall away and you will have

as the derivative of the tanh-function applied element-wise to your actions.
You then want to take the log of the following density

The scaling term c will persist, but due to the log you can move it out of the sum.

Here D is the dimensionality of your action space.
Now when you want to perform backprop, the term D log c only depends on the constants D and c. These are irrelevant for the derivative.
What does this mean for you?
You can use 6+4*tanh(u) to transform your actions between e.g. [2, 10] without having to change the entropy correction formula.
Source: This has been part of my master’s thesis.