I've heard that you can get efficient re-encodings, but that typically means torrenting it from somewhere. I'm not aware of a way to make high quality re-encodings locally without lots and lots of tweaking/testing/re-encoding and it takes a particular set of skills.
14TB+ hard drives are not too bad (~$235) so that would be 210 movies right there (though you are going to need to "burn" 1 drive for parity). The other option is to more liberally interpret copyright laws and buy the disk then pirate a copy that matches your requirements. Seeing how there are many people out there just doing the pirating step and that you aren't running a pay-for-plex scheme then I can't imagine you running afoul of law enforcement.
You don't even need backups for this, really. If you own the discs and lose the digital version, just copy it on the disc again. If you acquired it via other means, then... it should be possible to replace most such data. Even if you do choose to make backups, then that doubles your cost per terabyte at most.
Storage is really cheap, assuming you're fine with something that isn't a fancy ZFS/RAID array.
It uses HandBrake, FFmpeg, MKVToolNix, and MP4v2 with some custom tuned settings and has really good results from my experience.
But seriously, HTPCs of yesteryear are essentially dead due to Windows' terrible handling of Dolby Vision, Atmos, DTS:X, and HDR. Even though there are players that will allow you to get much better quality out of your source file on PC, the hassle of licensing and HDR modes is just absolutely not worth it.