Dear @dougleb,
There are a few things I would lie to point you to.
First of all, I would rescale the problem, as your mesh size is very small
Secondly, I would suggest you use DOLFINx, if you are new to FEniCS, as written in The new DOLFINx solver is now recommended over DOLFIN
There are many examples of diffusion equations in DOLFINx, including Diffusion of a Gaussian function — FEniCSx tutorial