A typical neutron star of $1.5M_{odot}$ is thought to have a radius of around 8-10 km. This is only a factor of 2 larger than the Schwarzschild radius for a similar mass black hole.
We know that more massive neutron stars do exist. The current record holder is around $2M_{odot}$. Most equations of state (the adopted relationship between pressure and density) for dense nuclear matter suggest that more massive neutron stars are smaller and therefore must be even closer in radius to the Schwarzschild radius.
So the premise of you question is basically correct. It is certainly true that when you deal with neutron star spectra you do have to apply significant general relativistic corrections to measured temperatures and the same corrections would need to be applied to any temporal variations.
Thus a time-variable signal from a neutron star surface will appear slower to an observer on Earth.
For the last part, I suspect that the scenario you propose is extremely unlikely. Rhoades & Ruffini (1974) first established that there must be a maximum mass for a neutron star under GR conditions, even if we allow the equation of state to harden to the point where the speed of sound is the speed of light. This maximum mass is around $3.2M_{odot}$. This sets an upper limit to the possible value of $GM/Rc^{2} leq 0.405$ (see p.261 of Shapiro & Teukolsky, Black holes, white dwarfs and neutron stars). This in turn sets an upper limit the possible gravitational redshift (and time dilation factor) of 2.29.
Beyond this point the neutron star is unstable and will collapse to become a black hole. In reality the limit is probably a bit tighter than that because most proposed equations of state result in neutron stars becoming unstable at finite densities and at masses quite a bit lower than $3.2M_{odot}$.
So I think the most time dilation you are ever going to see from a neutron star surface is a factor of $sim 2$.
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