Of course not. There are two "measures" of climate sensitivity.
1. Climate sensitivity to doubled CO2. This appears to 2.9 +/- 1.5 degree C.
2. Climate sensitivity to increased radiative forcing. This appears to be 3/4 deg. C for every 1 Watt per square meter of additional radiative forcing. Doubling CO2 adds about 4 Watts per square meter of radiative forcing.
The full atmosphere temperature increase directly attributable to doubled CO2 is 0.8-0.9 C. The rest is due to feedback, predominantely positive water vapor feedback.
You know these things.
And there is no reason whatever to believe the bootstrapped imaginary feedback 3-4.5 figure instead. And if there were, then there would be just as much reason to expect the equilibrium temperature effect of increased *solar* forcing, to be 3 to 10 times larger than you rightly insist it is.
Why isn't there a special new 3, climate sensitivity to modestly increase solar output, with a spanking new fudge factor of 3 times, allowing solar variation to account for all observed temperature changes? Because it is physical nonsense to tie a temperature change to a physical effect that does not have sufficient power to sustain that temperature change.
"Feedback" is in this context a weasel word for "additional power source besides the one we are alleging is a cause, since the one we are alleging is a cause is demonstrably too small to cause the effect we wish to predict".
If positive water vapor feedback is supposed to supply 2-5 times as much power as direct CO2 forcing - by your figures, mine say 3-10 times - then why isn't positive water vaopr feedback supposed to supply 2-5 times as much power as direct *solar* forcing? Is one supposed to be magically different from the other? (Both are supposedly operating through temperature).
Meanwhile, there is in fact no such observed and huge positive water vapor feedback. The reason is the atmosphere is largely saturated with water vapor. Yes it provides virtually all greenhouse power - but is also does so pretty constantly. Very little outgoing IR that can be stopped by water vapor isn't. And raising temperatures by less than 1C, isn't going to make a huge difference in the amount that gets out.
Clouds are global net coolers with a total power of 20 watts. If all of them drop out of the sky completely, then you can get 20 W to add to the 4 direct and that will get you 3-4C warming. But all clouds are not going to drop out of the sky because of an original temperature increase of less than 1C. In fact, best estimates of past changes in average cloudiness put it at 5% variations on a time scale of a few years, and more like 1% secular variation when those swings are averaged over periods more like 25 years.
Oh and also they are in the wrong direction. (Cloudiness has very marginally increased as temperature rose).
Past solar variation accounts for a quarter of a degree of past warming, concentrated in the first half of the 20th century. Past CO2 increases account for another quarter to a third of a degree. Both do so by the direct forcing and do not require non-existent mythical amplifiers an order of magnitude larger than the original signal. Combined, they fully account of actually observed temperature changes - with a climate sensitivity of 1. (SB law, no fudge, power goes as 4th power of absolute temperature).