Sally,
I don't know if this would help. You mentioned your son "tunes out" of books on tape. But something I always did with my daughter (non-LD) and something I'm insisting my son (LD) do is listen to books on tape every evening after reading, and as they are falling asleep.
The way I choose the "books" is for my son (he's 7) he gets shorter, simpler ones. I prefer old classics like "Cricket in Times Square," Folk Tales from various cultures, Greek mythologies, etc... I play the same story every night for about a week or two.
Although he doesn't get as much out of this as my daughter (yet!), I do believe it is helping with his listening, comprehension, vocabulary, auditory memory, etc...
For my daugher books on tape have done amazing things. She has always listened to stories above grade level and has an awesome vocabulary, auditory memory, etc... Now, she may have turned out this way even without books on tape. But I can't help but think that years and years of good literature and history listened to nightly has helped at least a little. (Also, there's nothing neater than a 10-year-old who can explain Greek mythology better than most college literature majors!)
This is just a thought and something you may consider trying until you can get started on LP or maybe after you've finished it. Particularly since it's easy, inexpensive and it makes a nice bedtime ritual.