The process of record linkage seeks to integrate instances that correspond to the same entity. Record linkage has traditionally been performed through the comparison of identifying field values (e.g., Surname), however, when databases are maintained by disparate organizations, the disclosure of such information can breach the privacy of the corresponding individuals. Various private record linkage (PRL) methods have been developed to obscure such identifiers, but they vary widely in their ability to balance competing goals of accuracy, efficiency and security. The tokenization and hashing of field values into Bloom filters (BF) enables greater linkage accuracy and efficiency than other PRL methods, but the encodings may be compromised through frequency-based cryptanalysis. Our objective is to adapt a BF encoding technique to mitigate such attacks with minimal sacrifices in accuracy and efficiency. To accomplish these goals, we introduce a statistically-informed method to generate BF encodings that integrate bits from multiple fields, the frequencies of which are provably associated with a minimum number of fields. Our method enables a user-specified tradeoff between security and accuracy. We compare our encoding method with other techniques using a public dataset of voter registration records and demonstrate that the increases in security come with only minor losses to accuracy.