The tire shop balanced my tires at 41 psi, when my recommended psi is 30. I have since lowered it to specification, but would this throw off the balance?
No. Balance is caused by even weight distributed around a tire.
If there is more weight in one spot the tire will "wobble" when spun.
Inflating a tire more may alter the diameter, but the weight of the tyre itself is still in the same relative place.
It won't affect wheel balance, but high tyre pressures will give you a much harder ride, so any bumps & stones etc.. even smaller ones may well be felt through the steering wheel and come across as vibration. Lower the tyre pressures to the correct specs, if you still feel that there is a balance issue just have the shop re-check the balance for you.