Singing actually helps because it makes you aware of where your voice is pitched and how it feels when it's resonating in different places.
Learning at least a bit of IPA (International Phonetic Alphabet) will help you recognize your problem vowels and know where to put your breath to make more sound (on the open, pure vowels). Vowels are vessels of emotions, consonants are vessels of ideas.
Keep a work list of words that you need to learn to repronounce.
Your recorder is your best friend, you've got that part already.
To get the effect you really want:
--get a tape that will give you exercises to rid your voice of regionalism
--remember straight men tend to only speak on one or two pitches. Their pitch tends to go in more or less a straight line, creating emphasis with volume and rate of speech only. Whereas gayvoice fluctuates all over the place pitchwise, with emphasis created with volume, enunciation, rate of speech, and facial expression.
--a well produced male voice tends to find its optimal pitch at about 1 1/2 - 2 whole step tones on the musical scale above the lowest note you can sing. For example, if low G is the lowest note you can sing, your speaking voice optimal pitch will be Bb or B natural. Don't fall into the gay trap of raising the pitch to get louder.
In addition to Linklater's FREEING THE NATURAL VOICE, recommended above, the other landmark text is Skinner's SPEAK WITH DISTINCTION.
For accents and reduction, recommended is Paul Meier, founder of the IDEA. There are people who love David Allan Stern, I'm not one of them, but you may want to check out his site too. Sam Chwat is dead, but you may want to glance at Tim Monich's AccentPros.com too if your accent is part of the issue. Some of these sites also have general voice and speech training modules that may be of help.