I just did some consultant work for a pan asian rest. and one of the desserts included a Thai basil-lemon green tea gelato. I've found that the herbal infusion lessoned the dry and earthy qualities of just the green tea. I'm sure that increasing the sugar content would make a difference I'm just not on board with super sweet. All I did was make my basic gelato recipe and then incorperated some green tea powder to taste. The big catch is adding the powder to hot liquid so that it blooms properly and also going for a little less than what you think you need because the flavor will intensify. On and easier note infusing your milk/cream with tea always works you just need to use more than what you would with water simply due to the muting effect of the fat in the cream.
I special ordered my powder from one of my specialty food suppliers. Living in San Fran it should be quite easy to find giving the large Asian population.
However try enjoyingtea.com and I'm sure you'll find just what your looking for. CHEERS