I used to have the litter boxes in the basement, and when I saw J.D. heading to the basement, I would quietly follow him and wait at the top of the stairs with my little cup. As soon as he started going, it was like he couldn't stop mid-stream, so I would walk down and put the cup in his flow and get my sample. I don't know if all male cats are like that. When I got real desperate for a sample, I would put the litter box right smack in the middle of the living room in plain view (temporarily, just for the one test), and wait for him to get in and start going and then approach him with the little cup.
Good luck restarting the insulin. Please keep us posted with updates.