Yearly changes of solar irradiation and atmospheric feedback
I think your ~2 figure for CO2 greenhouse amplification is in error. 
* In the last 200 years it's gone from the high 280s to low 400s.  This is an increase of about 50%  Good thing it's not linear as the previous greenhouse effect is overall about 18K.  If there was no effect, the earth would average about 0 C.
* As CO2 increases it takes more bounces for an infrared photon to escape.  But you get some degree of diminishing returns.  Doubling the CO2 doesn't double the greenhouse effect.

But to your question.

Right now we have about 1 degree of additional greenhouse effect.  Compared to the 18 degrees of existing greenhouse effect this is about 5%.  

I would expect that this is the factor to use.  So the eccentricity amplification should be about 5%  So 5.25K instead of 5.  or observationally 1.05 * 3.8K