Thank you all. You all helped get me on the right track (pun intended or not).
Got our three set of tickets. Compared the pricing and the Two Together Railcard was cheaper than BritRail for three trips in a month. Tickets were £137.40, £20.10, and £105.60 plus £30 for the card. BritRail was going to be $215 each plus $20 each for reservations (not sure those were needed, but seemed like a good idea). About $100 cheaper or $40 without reservation. These prices are higher than may have been available, but we wanted to leave about 8 or 9 each morning.
I booked through Virgin Rail. Within minutes, the BritPass is showing up on the Rails app and the tickets are showing up on the Virgin Rails app on our iPhones.
In other words we got a digital Railcard, so no having to pick it up. I've never been to the UK and for my wife it was many years ago; so won't find out for sure until we board the train. I did have to put in a UK address and phone number at one point for the Rails Card but assume it was for mailing a physical card which we're not getting. I did have a friend's address, but assume any legitimate address and phone number would have worked.
We didn't look at breaking the trip up as it was already enough to get all the tickets two weeks before leaving and we'd already booked all our rooms. We hadn't realized that getting train tickets was going to be so tricky and that we should have done it earlier.. This is much harder than our third world travel. But then the costs are so much lower that we don't worry about having everything in place.
Lastly I found the Man in Seat 61 site to be a good overview of the options.