ok, i just wrote a really long answer and it disappeared because I wasn’t logged in. So, quick answer now, because I have to leave!
I have a small physics background.. The frisbee generates enough lift when thrown horizontally to keep itself afloat, but doesn’t generate thrust, that comes from your hand and how hard you throw it. It travels far and keeps itself off the ground with its lift, and doesn’t lose its initial thrust quickly because its aerodynamic. However, when its thrown vertically, the lift force is now horizontal instead of upwards, so its not helping, plus you have to fight against gravity to push it up and the only force pushing it upwards is the initial thrust force from your hand. Therefore, my prediction would be that you can’t throw it any higher than other object of similar mass. so however high that is = your answer.