G650X stuck in Riga, Latvia, with blown head gasket, advice needed

[k1322]

Quoting my travel companion, as we are in a rather problematic situation.

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Hey I'm in Riga after turning back here from half a day riding in intense summer heat (32C) and noticing massive oil leaking from the cylinder head gasket area. My trip is possibly ruined one day in, but perhaps you guys can offer some thoughts before we head to the BMW dealer tomorrow.

Facts;
-I replaced the coolant before the trip but had trouble doing it. Might have done it improperly and I didn't check the thermostat.
-we rode really slow in sand, stopped often and the bike felt hotter than it ever had (but I never did stuff this hard in such heat)
-the thermostat light never came on, it also doesn't turn on when switching the contract on I noticed now. It does however consistently blink when using the engine kill switch.
-oil is leaking at an alarming rate, almost gushing down the frame. Almost looks like it leaks a drop a second when riding.

To me it sounds like a very unfortunate chain of events leading to a blown gasket or even a warped head...