That's great your beans popped. A little more info on what your medium is and why did you not just start them in that instead of taking the risk of hurting them when placing sprouts in medium. If your medium becomes toooo hot you can cook them. I never have used a dome but holding in heat can be good or bad depending on if you need it. I use 2 foot fluro's but cfl's would work. Some soft light is best for sprouts, they need it to make energy.

I have one proofed female papaya that is yeilding 50 or more clones a month. Too many for me so friends get setup. It can take time to get to the right spot for the numbers you need but once there and your set.