Thanks @Bertrand256 . I did actually stumble across these nodes. There are only three methods I need to call:
{"method": "masternodelist", "params": [], "id": 1}
{"method": "getblockhash", "params": [BLOCK_ID], "id": 1}
{"method": "masternode", "params": ["payments", BLOCK_HASH, 1], "id": 1}...