Viewstate
sent with each request and is still encrypted. You cannot store such large files in it. To speed up websites, there is the practice of turning off Viewstate
altogether.
If your files are shared between all users, then replace storage in session with Cache
storage.
You can also use a third-party cache service (memcached, redis, etc.).
To save RAM, you can store your temporary files on disk between requests. With a small amount of RAM, you will have to make a choice between performance (stored in the memory of any cache service) and memory load (stored on disk).
If the task allows it, you can try to alter the sequence of working with files eliminating the need for their storage between requests. For example, in the beginning we collect information about the processing of files from the user and only at the end apply all the algorithms to the data from the files.