Here's my guess -
Assuming long, you've got 35 inches or so in your bot to stow an arm. I'm also assuming you need to stay under 17.5 to go under the platform, which means you can't really "slant" you arm from front to back to get increased length while stowed.
This gives you a 3 foot horizontal bar. If you use that bar and hook it on the vertical tube, you can pull down on the end. With a tiny bit of clever engineering, you can "lock" the bar in place just using that torsional force, then spin your robot up and over it (inverting your robot) and placing it high enough to score - while only using the one motor to pivot the arm.
So, if you put another 1/2 length arm, hinged from the center of the bot, and put the motor at the end of that connected to the longer 35 inch arm, you could release the shorter arm, say 16 inches long. It will pop up on the gas shock. This plus your 16 inch height robot height is more than enough to get it above the scoring height limit. Then you simply click your horizontal arm into place against the vertical bar and invert your robot.
Tell me you're going to invert your robot. I'm drooling to see it
PS: This fits reasonably well. At 10 RPM roughly, you rotate 1 time every 6 seconds. 16 inches, the length of the shorter arm that rises from the center of your robot is about right for the torsional arm you'll be working with. It packages within the long driver base with an inch or two to spare too.