Looking for advice: courting other NPOs for possible merger

I am the sole remaining FT employee at my nonprofit. We still have a chunk of cash for our programs (approx 400K), but are burning through our unrestricted funds with overhead expenses. I've been tasked by the board to research nonprofits doing similar work in global health and to inquire about any potential interest in a merger, so that they may use our remaining funds to continue our programs (at least in part) and take on the operations costs.

I've identified a few orgs with similar missions. However, I am unsure how to approach them to initiate this conversation. Should I contact the ED? What is the best way to communicate? Email? Phone call? How much information do I offer in the initial communication?

Does anyone have experience with this process? Is it daunting? Any insight would be greatly appreciated.