It might work-- I've seen some reports in the past of people using H20 SIMS to activate on other AT&T MVNOs. I've also seen some folks claim that it might cause longer-term problems, even if it activates. I have no personal experience in re-purposing AT&T network SIMs. If you're willing to accept the possibility that you might have to replace it later if things get glitchy, I don't see the harm in trying: the website will either accept the SIM, or reject it.
I have used both callingmart & pinzoo.
Both have been fine in my experience.
Your first order with either may be delayed and require a subsequent step to clear their anti fraud systems.
A caution re callingmart is they add a fee to some brand refills and it is not clearly stated on the product page so be sure to check the final total in cart & before hitting the final pay button.
Callingmart almost always has a current coupon/promo code. Sometimes there will be a week gap but most of the time there is a valid code. www.callingmart.com/promo/
Just to be sure there isn't confusion: the GoPhone name was rebranded as AT&T Prepaid in 2017-- so you might have better luck looking for refills under that name. Callingmart still refers to them by the GoPhone name, while Pinzoo lists AT&&T Prepaid.. As far as I know, the 2 are actually the same product.