The V6 suzuki's have a heating loop on top of the Inlet Air Control.  If you overheat the engine it can blow the complex O ring out.  When this happens the motor sucks cooling water into inlet and further depletes the cooling water.  You may notice constant water dripping out of exhaust system also.  Seems that when radiator gets low enough to cause some cooling issues, the water seems to stop dripping from exhaust pipe.  When this was happening to me and not at home, I tried to bypass the heater system and run w/o it.  The motor ran like crap as it was then able to suck air instead of water and was running LEAN.
When I removed the cover on preheater/airflow indicator, I found the gasket blown out and stretched.  When trying to force it to stuff back into the groove it is supposed to fit in, it broke (of course).  Then it wouldn't hold air or water.  Attempting to fix with silicone sealer would not work.

I cut off the excess and slightly overlapped the breaks, then I took bow string wax (any wax would probably work) and scrapped the edges and filled around the O ring with the wax.  I started the motor and let it run a few minutes to let wax melt in, then retightened the top of IAC and filled with water.  O2's are working motor runs great, and cooling issues are gone.
I had to get the O ring from Suzuki, took two weeks.

Glad you finally figured out what was causing the cooling issues.  That took a while to figure out.

Pretty resourceful Birdhunter. Makes me glad for the simplicity of the 1.6 though 

Yes, I noticed the simplicity of your 1.6l.  I think you still have more room in engine compartment though I don't believe you could get any more in there.
At least it has made me much more knowledgeable about wiring issues, and problem solving.  And at my age it is easy to ignore how long some simple issues have plagued me.  And when it is running good, its even easier to forget.

I bet, there's no replacement for displacement. Yeah, I HAD a lot of crap in my engine compartment. Cleaned it out pretty good though when I swapped engines. Got rid of a lot stuff and tidied everything up more. I'll get a pic up soon. Still, now that you've got your V6 figured out I have to admit I am a bit envious. 

It's a Modification, and every Modification requires two more.  Sometimes we get to enjoy using them between modifications.

Displacement has advantages, so does twice the Hp + 5.  Of course you know that.
I don't have the wiring where it should be.  But last time I worked on it, I was at least three weeks chasing wiring only to find a connection that I hadn't touched loose enough to throw various intermittent codes.  Kind of like your problem only lots longer.  I spent so much time & energy on the Transmission codes I never got my cruise control installed, and I really wanted it.  Maybe good thing, because I have seen a steering wheel with cruise control and intermittent wipers.  That might be enough to get me back into wiring.

Buddy, you have the patience of a Zen Monk!  Wiring and electrical are like math to me, both give me big headaches. I'd rather grind metal anyday