I'd, inject some of my own JS into
random.org that takes their results and spits it into JSON
I'd then do the same to populate the other page. I dont know how I'd accomodate multiple sets of the quickpick numbers in the other form as I didnt look at what that side did.
First attempt at the inject would be to find the JS method that outputs the numbers, and add the line to spit into hash. I do this by copying the JS method add my code and pasting it into the Chrome console. Lovely custom JS.
All this hinges on accesible JS of course.