You can drink too much, according to other posts I’ve read here. It’s like any other probiotic. The more you take, the more dieoff you’ll get and generally you don’t want to have noticeable symptoms of dieoff, for your eliminatory organs’ sake. Cut back to a half or even a quarter and see how your die-off is. I actually use a ton of grains in mine, because they’ve been multiplying well, compared to what you are describing, maybe a quarter to a third cup of grains per quart. I would guess it doesn’t make it stronger so much as it speeds the time in which the grains digest the milk sugars, shortening the ferment time, which is definitely affected by temperature.
I don’t let mine go much more than 24 hours (but it is warm here right now, that may lengthen this winter) and my curds range in size from eraser tip to marble-sized. If you let them go too long, you run the risk of starving them. Are you letting them ferment at room temp? If so, I’d strain and drink or put them in the fridge after a day to a day-and-a-half, to prevent them from consuming all the sugars and dieing off.
I’ve seen people making this with both goats milk and coconut milk. I would imagine the taste differs some, but the probiotic benefits should be the same.