To ensure Screaming Frog can handle the crawl you could chunk up the site and crawl it in parts, e.g. by each subdirectory. This can be done within the 'configuration' menu under 'include'. There's loads of tutorials online.
You can also use exclude to ensure it doesn't crawl unnecessary pages, images or scripts for example on wordpress I often block wp-content
Definitely sounds like a problem with query parameters being indexed though and its often good to ensure these are addressed in the search console.
