Finally ready to switch my final windows device over to linux, but I'm running into a problem. NTFS drives aren't a good idea under Linux, but my 4 NTFS drives are this full. I own zero extra hard drives, and do not want to spend $300 on another one. 
How can I bring these files into Bazzite WITHOUT just wiping everything and re-downloading 10+ terabytes of movies, shows, music, games, and other data I refuse to delete?
You can use NTFS on Linux. Yes it can encounter problems eventually, yes the tools to fix it properly are only on Windows for the most part. But it works fine in my experience especially if you're mostly reading and not writing.
If that's not an option then you do need to move your files. You can either buy another drive or buy a temporary cloud storage plan (pcloud, google, many others offer 2TB for $9.99/month and 5TB for maybe twice that) and upload your stuff there on the monthly plan then cancel when done. To minimize danger even if you go the cloud route I'd upload one drive's contents at a time, wipe, reformat, download the contents, move to next drive. You can use something like Cryptomator (https://cryptomator.org/) to encrypt your files as you upload them if you wish and there's also 7zip with AES password encryption and encrypt file names though it requires duplicating the files in question which takes up space.
Another option would be freeing up some space, using that free space to create a new partition under Linux using a Linux file system, moving files from your existing NTFS partition there gradually in batches, shrinking your NTFS partition using Gparted or similar gradually while expanding your Linux ext4, zfs, etc partition as you transfer them in batches. Do this for each drive. It'll be a pain in the ass for the fuller drives and there are no guarantees doing this kind of resizing and copying couldn't cause something to break. But it is free. I would suggest another drive or going the cloud route at least as back-up if you're trying this.
The games in particular you may want to reinstall through Steam, Lutris, Heroic launcher, etc though I guess you can deal with that when you get there. The only reason I'd keep the games themselves as opposed to just their save files and any mods I have would be if I'd done modding that altered the game files.