Oops - I see your post above mine. Ignore the below if you wish. But, there is an option that allows you to print paper tickets at home and carry the tickets on your phone. At least you might consider what I have written the below.
If you are comfortable using apps and Wallet tickets, I have very successfully used the LNER website or app to order tickets from the US - multiple trips and train tickets in the last 6 months. I've purchased LNER tickets and tickets for several other carriers - LNER has been the best website I've used for purchases. Tickets come in an email download and are in your account on the app. I have printed off the tickets before leaving the US, but have never needed to show those - I always had reception and could show the Wallet tickets or could have gone back to the email if necessary.
An advantage of having an app with account set up is that when in England, you can easily purchase additional tickets if necessary (emergencies, change of plans, etc). I had to do this a couple times, literally standing on a platform. No manned ticket kiosk, I suppose I could have used the machine, but a familiar app was easier.
We had one of our trains over an hour delayed and a second train canceled last month - we got refunds very easily from two different carriers. Having all the ticket info stored in "My Account" was quite helpful for pulling the required info on the journeys.
I have also successfully used the Southeastern App. I couldn't get Southwestern to work either in the US or the UK.