The process that you described can be also used with Miniconda. We have a document that describes copying one installation to different LPARs in details. I want to note that Miniconda is a flexible tool, and it can be adapted to different environments. We didn't want to limit customers to only the maintenance approach. If you feel that you need guidelines on how to adjust Miniconda to your environment, don't hesitate to reach out to us.

How to deploy a specific level of tools to one LPAR?

Let's start with understanding what an environment is. From the perspective of filesystem a conda environment is a directory that contains a specific collection of conda packages that you have installed. During installation process conda installs dependencies and confirms that there are no incompatible packages in the environment, so the end user doesn't need to worry about that.
From the user's perspective, a conda environment is a set of tools which will be used together (not necessarily simultaneously). We would recommend creating a separate environment for test purposes (see Early testing of updates) or when you need 2+ levels of tools on one LPAR.
So how to deploy a specific level of tools to one LPAR? Create an environment, activate it and install required packages (all verbs refer to conda commands).

Which files does miniconda modify?

miniconda-zos-X.Y-yyyy-mm-dd.run is kind of a self-extracting archive, which will be unpacked to the directory specified by user. It is called the Miniconda installation directory. When you install a package into an environment conda will modify an environment directory and a cache directory, which by default are placed into the Miniconda installation directory. Also, conda can create and modify $HOME/.condarc and $HOME/.conda. This file and directory are located outside of the installation directory.

Conda doesn't modify other external files or directories unless the user explicitly specifies that in configuration files, conda command options or any other way.

Note, that the tools that you install with conda can modify external files. This behavior is unrelated to the Miniconda installation approach.

Normally, environments are created within the Miniconda installation directory. Although it's possible to make an environment on a separate zFS, at the moment we don't recommend this approach, because it might lead to the further issues with updates.
Note, that you will need a Miniconda installation on each LPAR where you want to use environments.

Please, let us know if you need further assistance.