Based on your idea, I implemented a 3 bit CRC last night.

Since my word list is 4096 words, each word represents 12 bits. This means that if I use a 3 bit crc, each word can check 4 other words.

    { words: [ 'beg', 'notably', 'renew', 'curious' ], crc: [ 'joy' ] }
    { words: [ 'beg', 'notably', 'able', 'curious' ], crc: [ 'joy' ] }
    [ '100', '000', '011', '000' ] 100000010000 
    [ true, true, false, true ]

You can see it correctly identified that the third word is wrong. I will probably integrate something like this next time I update wherewords.id, although that might be a while....