No, I am not affiliated with either.  I have been mentioning them because reducing S-risks seems like an extremely important cause, yet S-risks seem to be highly neglected within the Effective Altruism community.

Are they currently funded by any large EA donors?

The Center for Reducing Suffering is definitely underfunded.  To quote them directly: "As a small, early-stage organisation, we currently operate on a very limited budget; in fact, we only recently started paying researchers at all. The marginal benefit of additional funding is therefore particularly large: we have much room for funding, and funding at this early stage is critical for enabling CRS to get properly off the ground. the same amount makes a much bigger difference at this stage, compared to a more established or less funding-constrained organisation."

The Center on Long-Term Risk has significantly more funding.  CLR has an annual transparency report where you can see their financial information. Open Philanthropy also recommended a $1 million dollar grant to the Effective Altruism Foundation, the parent organization of CLR.

Is funding a bottleneck, such that more funding would result in better results?

More funding for S-risk research could potentially result in these organizations being able to hire more people and acquire more top talent. In the case of the Center for Reducing Suffering, as mentioned above, they are an early stage organization with a lot of room for funding.