High lift drums, Full Vertical drums, there are a lot of different types. I have two high lift doors and the drums are about ten inches as I recall. The size is caused by the tapered design; they are made this way in order to alter the mechanical advantage of the cable as the door travels. With a regular door, the effective weight of the door decreases as the door is raised; the top turns horizontal immediately when it's raised, so the spring load gets lighter as the door goes horizontal. Because the spring is relaxing as the door is raised, the straight drum works well.
With a high lift, the first few feet of opening, the *entire* weight of the door is constant; the door doesn't get lighter until it turns the corner. With the high lift drums, the cable runs in a groove along the taper controlling the position of the cable and its "leverage" vs the spring. The leverage is greatest when the door is down, decreases as you open the door and when the top of the door starts going horizontal, that's the point where the cable reaches the straight portion of the high lift drum.
The tapered drum is required because a straight drum can't be adjusted to work with a fixed door weight through a portion of the travel because the springs are not a constant.
Besides needing to make room for the drums themselves, another necessity is clearance for the cable; with the tapered drums, the cable hangs very near the corner formed by the wall and the door track with the door closed. As the door is raised, the cable position follows the taper and moves both away from the wall AND away from the track, causing (on my doors) the cable to rub the top corner of the upper panel as it tilts. Because of this I have wished the track was even *farther* away from the wall.
The diameter of the drums requires a different spring mount as well as larger springs.
The picture of your setup indicates that you might need to make a few changes(!)
This pic: a full vert, a high lift,
And below them a standard drum.

Note that even the straight drum is built with a slight taper.
Edit to add pics of two 10x10 doors, both commercial, insulated, one is standard, one is a high-lift.
