Firstly it is normal to get steam coming out the exhaust (by product of combustion) especially on a cold day and when starting from cold.
There are 2 hoses to the coolant tank - a transparent hose to dump excess coolant and a black hose the goes to the filler cap. Is the filler cap fitted correctly and working? It has been known for the caps to fail so they open at a lower pressure - if memory serves me well, the same cap is used on a variety of Japanese car radiators which may make it easier/cheaper to source another to rule that out.
Before tearing the heads off, have you tried:
The CO₂ leak tester kit is designed to check for the presence of combustion gases in the engine coolant. It should be performed when signs (overheating, bubbles in the coolant, rise in coolant level upon starting) point to a blown head gasket, cracked block, or cracked cylinder head.
How does the test work?
In the case of a damaged gasket under the head or the head itself, part of the combustion gases containing CO₂ goes to the cooling system, at this point they react with the liquid and change its colour.
eBay search for: Combustion Leak Tester Kit Detector Head Gasket Block 30ml Fluid Petrol/Diesel