Continued...
Thirdly, you state, “... those who say the current warming is "just a natural cycle" would be best avoiding mentioning global cooling at all because we aught to be be moving into a cool phase by that notion yet the planet is definitely heating...”
Again, I have to disagree. For the obvious reason that weather is not climate. When you say that the the planet is definitely heating, where is your baseline? To measure anything, you have to have a baseline from which to measure. I'm not suggesting that the earth's climate isn't rising relative to recent measurements but if your baseline is a very cold period (say, the little Ice Age) then it's pretty obvious that today is warmer than, say 1849, when market stalls were erected in the middle of the frozen Thames.
The last Ice Age was only about 15,000 years ago. That might seem like a long time ago but when viewed on a geological time-scale, it's the blink of an eye. I would tentatively agree that the earth is warming (if we take the end of the last ice age as a baseline) but the rate at which it is doing so and the degree to which this is true is statistically insignificant.
It is a curious fact that even though we're dealing with climate which is the scientific equivalent of geology in terms of time-scale, the climate change advocates seem to think that the last hundred or so years is somehow unusual and important.
You say the planet is warming. Warming relative to what temperature in history? And is that warming greater than at any time in the past or is it warming at a faster rate than at any time in the past?
I don't think that it is, as I have not seen any evidence to substantiate that specific claim.