So I take it that you have also checked the oil filler cap for emulsified deposits?
Have you had a "sniff test" in the coolant expansion tank? Easiest way to eliminate a head gasket failure and only takes a few minutes to check! My money would be on head gasket failure..... But... It has to run damn hot on TS's and V6's too get anywhere near failure, I drove thirty miles with a busted radiator and didn't even cause any head gasket issues on my old TS,so!
There is always a cause to a problem! Simply changing the headgasket may cure it temporarily but it may come back.
How long has the coolant loss been going on for? Has it got any worse over time or is it constant? You could have a leaky radiator/ hose or thermostat housing.... Look for crusty deposits around the ends of hoses and the thermostat.
You may not see it because of the engine undertray but even a slight leak from the radiator will not drip all over the driveway, it may well be slight steam under pressure when driving at normal temperature, don't expect clouds of the stuff, that's too obvious.
Is your front carpet dry under the dash etc?
Leaky matrix maybe?
all these are good places to start looking mate
Oh one last thing, Your missus hasn't been putting oil in the expansion tank by mistake? It happens more than you may think!!!