Can I publish the accumulator trapdoor and still keep it secure?
I guess you are missing something. 

If you know that the accumulator value is $a=v^{\prod_i x_i} \bmod n$ to a set of values $x_i$ and you know the factorization of $n$, then it is easy to for any arbitrary $y$ relatively prime to $n$ (in RSA accumulators you accumulate primes) a value $k$ such that $y\cdot k \equiv 1 \pmod{\varphi(n)}$ as the value $\varphi(n)$ is public. So anyone can pretend that any arbitrary value $y$ has been accumulated using $a^k$ as the membership witness and note that the verification $a\equiv (a^k)^y \bmod n$ holds.  I guess that you would not like to have that "feature".

So either you make the factorization not public (use a trusted setup) or if this is not possible you can go with trapdoor free RSA accumulators (basically by computing an RSA modulus in a way that the factorization is unknown to anybody).