I had the same issue just the other day. I wound up just searching through the entire object and accounted for both lists and dicts. The following snippets allows you to search for the first occurrence of a multiple keys.
import json
def deep_search(needles, haystack):
    found = {}
    if type(needles) != type([]):
        needles = [needles]
    if type(haystack) == type(dict()):
        for needle in needles:
            if needle in haystack.keys():
                found[needle] = haystack[needle]
            elif len(haystack.keys()) > 0:
                for key in haystack.keys():
                    result = deep_search(needle, haystack[key])
                    if result:
                        for k, v in result.items():
                            found[k] = v
    elif type(haystack) == type([]):
        for node in haystack:
            result = deep_search(needles, node)
            if result:
                for k, v in result.items():
                    found[k] = v
    return found
deep_search(["P1", "P3"], json.loads(json_string))
It returns a dict with the keys being the keys searched for. Haystack is expected to be a Python object already, so you have to do json.loads before passing it to deep_search.
Any comments for optimization are welcomed!