Let me clarify,what I want to know is
(a) 'An established monastic order' - This the Goenka school is not.
(b) With principles and beleifs and aims as close to the Goenka school as possible?
(a) 'An established monastic order' - This the Goenka school is not.
There is no Goenka School. Generally this is referred as the linage of Saya Gyi U Ba Khin and Ledi Sayadaw U Ñanadhaja. Also it is influenced by Webu Sayadaw
Ledi Sayadaw U Ñanadhaja and Webu Sayadaw are Buddhist monks. Also there many teachers who are Buddhist Monks who are particle according to S. N. Goenka.
(b) With principles and beliefs and aims as close to the Goenka school as possible?
Many of the references in the disclosure are meticulously referenced from the Tipitaka. So any monastic order which practices which is close to the Tipitaka would share the same beliefs.