I'll be back, passing through, in early August, and would like to add
some Pre Pay value in advance for use then. But, apparently, I have
no idea what the answer to the "Security Question" on the registration
form is. Is there any way to get an online account without that
information?

No. But its probably your mother's maiden name.

And even when I get in, will they accept US-based credit
card details?

Yes any credit card would be accepted.

You should note that you have to pass through the barriers of a station
you specify during the seven days after you top up online or the Oyster
will not be updated and the money will be refunded to your credit card.
In other words you need to top up the day before you leave the US
and nominate the first station you are going to pass through.