Confirmed that the 380 has a blown head gasket. Combustion pressure in the cooling system.

It runs, clearly with one dead cylinder. When the revs are right down, the steam pulses are in time with the misfire…
I am currently pondering whether to fix it straight away or just pull the motor & box out and leave it in the shed for a while. Third option is to actually give the engine a rebuild - a rebuild kit is $800 including delivery, which seems pretty tempting.