It may and probably will be an improvement doing it the way you are, it really depends on the tenacity of your slime, and the composition of your products. The thing is, how will you replace the bennies when they starve and die after a few days? Adding more powder every few days would seem overly expensive, and it not guaranteed to activate all of the bennies. Now, the mutualistic fungi is fed by the roots, so they will not starve, but all of the bacteria and other types of fungi will. If you try to add food to the res to feed the microbes, you will feed the slime. Considering this, and considering that great white will only offer more bacteria (your products already have the fungi needed) it doesn't seem prudent to add great white.
Brewing the tea couldn't be easier or more appropriate in your situation. It's your call and you may be fine, but the attitude of cutting corners in any aspect of growing often leads to reduced yields and wasted time in the end.