Having the exact same issue with my moms 07 torrent. I spoke to a very reputable radiator shop that I deal with both for personal vehicles and my work fleet and they told me that chances are that the head gasket is gone.
Bleeding the cooling system on these is NOT fun. Point blank. I've heard even with a vacuum powered system, it is still a huge PITA. All I do is start the car up, heat on. Let it get to just below half on the gague, then hold the RPM'S just a bit below limiter for 30 seconds, let sit for another 30, repeat for ten minutes. Shut off, let cool down for 30 mins, start it up, let it idle for an hour. Seems extreme, but that's the best method I've found so far. I do undo the heater hoses, and fill the heater core up with coolant through the upper hose and then reattach it. Do NOT use the water pump bleeder, in my experience, it's useless and it's not the highest point in the system.
Her heater core went four years ago, went a winter with about 2/3 heat capacity but coolant smell in the interior and having to top off with less then half a quart weekly ever 60-80 miles or so. After doing the heater core, i had no heat at all, and the car was still consuming coolant. I replaced the heater core again, thinking I got a defective one, and low and behold I didn't tighten the HVAC box behind the dash all the way. Tightened it all back up, reassembled, after checking every fastener 10 times, no joke.
Start it up, sure enough no heat. But had a gurgling/surging noise coming from my reservoir. Now, we've owned the torrent since 2011 at 92k km's. We have done the vast majority of repairs in this vehicles life time, including coolant service. We only used dexcool 50/50 mix. No green, nothing but dexcool. And no sealers or additives. When we flushed it, we did it with prestone chemical flush and distilled water.
The shop I spoke to said that they don't always spit the coolant out of the exhaust via white smoke, and you don't always have tell tale signs, but most of the time, its the surging in the tank, wont be able to bleed the cooling system and constantly having to top it off, all of which we're currently experiencing, in addition to no heat in the cabin, but it's june so we could care less.
I am not looking forward to repairing it and doing the head gasket, but I've already done it on my 08 equinox twice, thanks to the rocker arms stripping out even when using a heli-coil. But it is easier than the older montanas, rendezvous and grand ams and what not. There is a lot more working room. Gasket kit is about 300 depending where you go and what you get. I spent about $400 CDN total, on fluid, oil, filter, plugs, gaskets, bolts and a few other little odds and ends ("while you're in there" kinda stuff). No timing chain/cam stuff to worry about aside from the rocker arms and pushrods, but as long as you put the pushrods back in the right place, and you torque everything to spec, there's really not a whole lot to it compared to other engines, at least IMHO.