Why not increase the growth rate across the board, and add facilities/research that can increase the growth rate dramatically. Things like Hospitals, Fertilization centers, cloning centers, Health and Human Services dept., terraforming, life extending/enhancing drugs...etc..etc...
The answer does not lie in depleting the Homeworld of it's citizens, rather it lies or should lie in developing your new colony's IMHO. Also, researching the income and maintenance saving tech's would help...maybe increasing the number of these.
"Tho' much is taken, much abides; and though we are not now that strength which in old days moved Earth and Heaven; that which we are, we are; One equal temper of heroic hearts, made weak by time and fate, but strong in will." -Tennyson