Dear Mr. Lovick: You are correct.
I've also read some of the books you mentioned (& maybe another dozen about HH over the years, only a few of which I still have on hand, unfortunately)
--it IS true: I honestly can't say specifically when I formed the idea that he'd have a heavy european accent.
--Did I mix him up with other long ago stories about say, Malini, and just ASSUME that since he was born outside the U.S., and his parents didn't speak english very well that he'd automatically HAVE to have a heavy accent...or did I hear/read it somewhere? Hmm...
So far, the one quote I can find about his accent, right-off-the-bat is from Bert Sugar's Foreword in his book with Randi, "Houdini, His Life and Art", a copy of which recently went for $9,999 on ebay ;)
"His stage voice was practiced, with strong enunciation given to almost every syllable; he reminded some listeners of a barker and sounded to others like a man with a slight German accent. His manner was straightforward, even quaint, with none of the suavity of other magicians, and often he signaled the end of a trick with a conventional 'Will wonders never cease?' "
Only a "sleight German accent" mentioned there...I'll keep looking.
P.S. & I'm going to use "will wonders never cease?". Great line.