Well, ignoring the fact that the largest contributors to greenhouse gases are all in the stratosphere, inert gases can make it all the way to the ozone, because they don't react with anything and only when they react with something do their weights actually change comparatively. But you are correct, they do keep adding "blankets" to the atmosphere. But the problem is that it's not likely to be the gases we release that tipped the climate change, but the energy near the glaciers that did.
What is happening is the energy from the sun would shine on the light side heating it up. Then at night the heat would radiate back into space. Greenhouse gas traps the heat so not as much can radiate back out into space, it doesn't matter where its position in the atmosphere is really, only that it traps the thermal energy.
The Oceans adsorbed this extra energy for so long because it's like a giant heat sink, but is gradually causing it's temperature to rise. So it is energy in the Ocean but its spread out by the currents . It is natural for the Oceans to absorb some heat and spread it around but when the overall temperature rises, it causes glacial melt.
I think they say it is 1-2 C above nominal and climbing.
When it reaches or by the time it reaches 6 C above normal we will have a complete glacial melting and the oceans will rise by as much as six feet or more. This would be disastrous to places like Manhattan, New Orleans and Venice etc.
But we have found a worse problem than the man made parts.
Frozen methane at the bottom of the ocean. Its a worse greenhouse gas than carbon monoxide,and it is starting to melt at the bottom of the sea. We may not have glaciers much longer.