An easy way to solve this is to repeatedly loop through the list of monkeys and update each monkey if it's a number or its predecessors have already yelled. Everytime a monkey yells their value, we set the changed variable to True to signify that there was an update. If the changed variable is False after looping through all the monkeys, then no further updates are possible and we stop the loop.
An alternative solution is to consider the monkeys as a directed graph, where the monkeys with numbers are leaves and the rest of the monkeys point to the monkeys that they depend upon. Then, you can run a topological sort to produce an order for traversing the graph once.
An observation is that changing the value of your monkey, humn, is directly correlated with the root monkey in a way that makes binary search possible. Specifically, increasing the value of humn will decrease the value of root, and decreasing humn will increase root. Note: depending on your puzzle input this may be the other way around.
Using this observation, we can perform a simple binary search and repeatedly loop our part 1 code with the humn variable initialized to our current binary search value. Once we find a value that satisfies root's equality, we're finished.
You can also use a symbolic solver such as z3. You have one unknown variable (humn) and you want to satisfy equality between root's numbers.
Fun problem with lots of alternative solutions. It turns out that using floating-point division (/) and integer division (//) in Python produced slightly different answers on some problem inputs -- be careful!