Derivation of Surplus in Paul Romer's paper on "mathiness"
I think you have a typo in your  $q_0$: the exponent of $N$ should be  $-\frac{b}{a+b}$. I did the whole calculus with this corrected type of $q_0$ and I was able to replicate your results (this is why assume $q_0$ has only a typo and you actually did the algebra with the correct $q_0$).
I suggest that the discrepancies to the paper are indeed connected to the Surplus function. But i cannot come up with any idea why this surplus function might be wrong.

Edit: Outside from the typo there was no error, @actuarialboi9 and my humble self calculated the individual surplus. If one multiplies that Surplus function with $N$ the number of people in the market results will be equal:
$\begin{equation} S= C(a,b,m) N^{\frac{b(a-1)}{a+b}} \;  \cdot \; N \;  = \; C(a,b,m)N^{\frac{a(1+b)}{a+b}} \end{equation}$