How to attack RSA-CRT with large public exponent?
There is a paper by Daniel Bleichenbacher and Alexander May called "New attacks on RSA with small secret CRT-Exponents" (you can find it under http://www.cits.rub.de/imperia/md/content/may/paper/crt.pdf). They are not quite able to break the RSA under your assumptions. I'm not aware of better results, but I didn't look at the list of articles citing this paper.