Repeated hashing is notoriously difficult to parallelize as it's naturally a serial operation, that's why we use repeated hashing as a Key-Derivative Function to protect passwords. For humans it's more challenging, since SHA-256 has 64 rounds internally, which means: to calculate a single hash, you need to iterate over the data 64 times, each time using the output of the previous round as your input.

What you can do, is:

(1) Optimizing the process of calculating a single round. I guess you can identify all the needed arithmetic steps (mostly logical opeartions and bitshifts) and divide them to multiple units of task-forces, assembly-line style, like a human-powered ALU. Ideally, workers that doesn't care about "which round it is", but only care about the computation itself should be as many as possible, i.e. using combinational logic instead of sequential logic.

I think many computations were done in this way before electronic computers, I believe even numerical simulations of fluid dynamics were done by rooms of female workers with mechanical computers running the same algorithm again and again over a matrix.

(2) Create as many copies of your human-ALU as possible. Although iterations within a single-hashing operation is not parallelized. But mining only requires you to do independent hashing, so it should scale linearly.

I don't have the needed skills to get an actual number, if you - the reader, thinks you can. Please do it and submit your blogpost to Hacker News.