Would this method work for generating sustained arbitrarily high time dilation in the center? Let's say we have a series of a large number of spherical shells.
Each shell has twice the mass and radius as the last.
There may be thin poles or ropes to make sure inner shells don't move around.
Each shell has a mass equal to $rc^2/2Gx$, where $r$ is the shell's radius and $x$ is between $3$ and $4$. $x$ is the same for each shell.
The shell's are assumed to have material strengths very close to the fundamental limit.
It seems to me that as travel inwards the Time dilation will exponentially each time you pass a shell.
Additionally the forces involved should be small enough for materials with finite strenghs to prevent collapse.
Is this correct?
 A: If we rearrange your equation to find the radius we get:
$$ r = \frac{2GM}{x c^2} = \frac{r_s}{x} $$
So if you take for example $x = 4$ as you suggest that means the radii given by your equation are smaller than the event horizon radius and therefore the shell wouldn't be stable and would collapse into the singularity.
I wonder if you mean $x = 1/3$ to $1/4$ i.e. the shell radius is $3$ to $4$ times larger than the event horizon? If so you could certainly construct a series of shells like this to make the time dilation at the centre arbitrarily large without the system ever forming a black hole. You would just need to make sure that the total mass of the shells never exceeded $r_\text{outer}c^2/2G$ where $r_\text{outer}$ is the radius if the outermost shell.
But you have chosen an unnecessarily complicated way if doing this. Simply construct a single shell with a radius only fractionally bigger than the event horizon and you can achieve the same end result. There is no need to nest shells within the outermost shell.
