I only use the A-MAZE-N unit. I have a pellet/dust maze, a 6" tube, and a 18" tube for long smokes.
This time I used the tray. I take the smoke box out and set it right next to the hole in the bottom of the smoker to get as much air flow as I can. It ran fine for a good 4 hours and then the smoke did go out on me. I think that I need to get one of those aquarium pumps like the Bella smoker has and position the tube to blow some gentle air on the tray/tube to prevent it from going out.
Even with the tray, you have to be careful not to get the heat up too high as the tray/tube alone will get you close to the 90 degree range where your cheese will start melting.
I don't have a cold plate, but I do use frozen soda bottles on the very lowest shelf to help keep the heat down. You can use a tray filled with ice too, but you have to make sure that you seal it really tight because you don't want the moisture from the melting ice to get into the smoke chamber as moisture on the cheese is not good.
I give mine a fairly good does of smoke for 4 hours to get a good deep smoke flavor on the cheese. But, if you do this it will be pretty strong right out of the smoker, so packaging and letting the smoke flavor penetrate into the cheese and spread out more evenly is necessary. If you try a piece right out of the smoker, you will think that you ruined it, but you didn't. It just needs a good two week rest. And for hard cheeses, the longer you can let them age in your fridge the sharper that they will become. I have some aged cheddar in the bottom of my fridge that is over two years old. I only share that with VERY special people.
The string cheese on the other hand should be eaten fairly quickly after the two week wait. I would say you would want to eat it within a couple months or so as that will not age like a cheddar.
I am not a cheese smoking expert by any means, but I have smoked a fair amount of it and really enjoy it. Pairs really well for a wine tasting if you like wine.