Time Dilation and Particle Decay
If you use the equation of the Schwarzschild metric.
$$ds^{2}=-(1-\frac{2M}{r})dt^{2}+(1-\frac{2M}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}$$ 
(equation 11.1 from Schutz's book A first course in GR).

If we think the neutron stay at rest in $r=r_{S}=2M$ then between the born and dead of the neutron $dr=0$ and $d\Omega=0$, and $ds$ will be the proper time, which I will call $\tau$ (I'm folowing the convention $c=1=G$).

Putting this on the metric we have

$$  d\tau^{2}=-(1-\frac{2M}{r})dt_{obs}^{2}$$

$$  \frac{d\tau^{2}}{dt_{obs}^{2}}=-(1-\frac{2M}{r})$$

and if we put $r=r_{s}$ (where the neutros was), we have

$$  \frac{d\tau^{2}}{dt_{obs}^{2}}=0$$

Then $\Delta t_{obs}=\infty$ . 

I couldn't write a comment that's  why I answered, but I think you had some mistake using the red shift equation to get the wavelength difference.

Can you show your calculus? May be I can help.