Two paths I see for the future of the Order after losing the war with the BHG:
a) Enters an alliance with the Red Dragons after withdrawing from Toledo. Order operations continue in the Omicrons, operating out of Omicron-100. The jumphole from Minor to Omicron-100 collapses. BHG sets up shop on Toledo, much to the chagrin of Liberty. Corsairs are no longer allies but are placed in a neutral status in Order diplomacy. The Order remains hostile to BHG, but interaction between the two parties is significantly lessened.
or
b) Order enters ceasefire negotiations with the BHG. Talks are brokered by the Zoners. Both the Order and the BHG become more pragmatic concerning the Nomad menace. The Order thus rationalizes that an agreement with the BHG is a more constructive path in dealing with mankind's worse enemy in Sirius. The BHG, realizing the extent of the looming Nomad threat, is ready to relinquish its own exclusive claims on all Nomad technology.
The BHG, having more leverage in the negotiations, would pressure the Order to nullify the alliance with the Corsairs. The Order would insist on overseeing all studies concerning the Nomads. Both parties agree to share intelligence on the Nomads. Both parties agree to share base privileges. There is no technology/vessel exchanges. The Order and BHG would have neutral relations to one another.
Both paths need increased Keeper/Wilde activity to make any sense.