If you have a Starbucks near you, go there and ask if you can buy a few of their Venti cold beverage clear cups from them. They will probably ask how many, you say "like 4 or 5" with a slightly questioning look on your face. And chances are they usually just give them to you, then you tip them something.
They also have one larger called a Trenta, but it isn't too much taller than the Venti, just fatter(which is how we become if we were to have one of their iced treats in that tanker). They wouldn't sell me the Trenta, my guess is they don't stock a lot of those cups.
The Venti cup is 6.5 inches tall. If you really needed, you could do some fancy cutting and tape work of a second cup onto the first cup; basically adding an extension and making it taller. Do what you have to do to get those roots under the medium at least an inch or two. And in the future, cut your cutting to a manageable size before you initiate your rooting process.
Hope that helps and good luck.