Can a producer who was paid a 'for hire' fee to produce songs try and copyright them as his own? How?

Based on what you say (e.g. you filed for a copyright and embedded your work in tangible media) you should have a likelihood of winning a lawsuit or settlement. I'd suggest you engage a copyright attorney since the things you relate involve contract and copyright law.. If you have good reason to believe your work is valuable, you might be able to find a copyright attorney who will handle your case at least partly on a contingency basis (e.g. some combination of fees and a portion of your later receipts).

If you have your "work for hire" agreement on paper and the producer signed it, you alone own the copyright on each production. If it's not in writing, you own the copyright to the song but he may have a claim to the production of the song. Complete your registration of the composition and attempt to register the recording. You and he may have to register as joint owners of the recording but he has no claim to the composition.

It all depends upon the written contract for the work. The following comes from the US Copyright Office website - www.copyright.gov: Copyright Registration of Musical Compositions and Sound Recordings For copyright purposes, there is a difference between MUSICAL COMPOSITIONS and SOUND RECORDINGS. A Musical Composition consists of music, including any accompanying words, and is normally registered as a work of performing arts. The author of a musical composition is generally the composer and the lyricist, if any. A musical composition may be in the form of a notated copy (for example, sheet music) or in the form of a phonorecord (for example, cassette tape, LP, or CD). A Sound Recording results from the fixation of a series of musical, spoken, or other sounds. The author of a sound recording is the performer(s) whose performance is fixed, or the record producer who processes the sounds and fixes them in the final recording, or both. Copyright in a sound recording is not the same as, or a substitute for, copyright in the underlying musical composition. Registration of a Musical Composition and a Sound Recording with a Single Application Although they are separate works, a musical composition and a sound recording may be registered together on a single application if ownership of the copyrights in both is exactly the same. To register a single claim in both works, complete Form SR. Give information about the author(s) of both the musical composition and the sound recording. Go see a lawyer with a copy of your contract with the producer.

The U.S. Constitution provides that the Copyright to the works created belong to the Author. It is not clear from your fact pattern, whether the Producer wrote the music or is merely the Arranger. The Composer would have paramount rights here. However, the Composer may assign on otherwise dispose of this Copyright. It would appear that in this instance everything will hinge on the Agreement between you and the Producer. Hopefully, you were represented by competent Counsel. You may need to enforce the Agreement in a Court of Law. Good Luck!