You are completely correct about M, all I did was add up 7p and 7n apparently, haha. I blame 2 AM. But yes, you are right, and after recalculating I also got
E_rot = 5.28692e-4 eV,
with the values of m_p and m_n being the ever-so-slightly different values given in the book. Either way...
I think you're making this way more complicated than it has to be, Yroyathon. I believe we have the same book, because most of the problems you ask questions on, I have been assigned as well. In this case, I used your original
E_rot = [l(l+1)*E_0*m_e]/(4*M)
The value of E_0 is 13.6 eV...