The Petzl STOP is for ropes 9-12 mm. 1/2" 12.7 mm, but for the practical sake of a device, it's 13. You might be able to stuff the rope in the STOP. Just expect extra resistance in use. This will suck the life out of what you want, which is upper-end performance.
Here's the scoop on that and other questions,
direct from Petzl.
Remember, Petzl caters to cavers first and rock climbers and search & rescue next. These are all SRT disciplines using 11 mm primarily. We adapt their gear to our needs, which is generally 13 mm DdRT. Other than the tons of gear we buy from them as an industry, they kinda otherwise scoff at our DdRT - 13mm hitch methods.
They only have two classes of descender (See below). There's a quasi-class in between that the rock and mountain climbing crowd favors, but they don't use it for climbing/descending; they use it as a belay device. Technically, what we do in the trees is self-belaying, so it stands to reason those cllasses of devices would work for us. Abseiling might just be a moment here and there, all day long. At the end of the time working aloft, you abseil out. True rappelling occupies only a fraction of the overall time that a treeguy would spend climbing doing pruning and deadwooding.
Self-braking decenders speak to the tree climber who grew up on friction hitches, that's because that's what a friction hitch does- it self brakes. Take your hand off the hitch and weight the rope and the hitch locks down. Same for self-braking descenders; self-brakes.
And ascenders for that matter, do that, the difference being the descender does not live in permaent hard-lock as does the ascender.
Standard descenders, you take your hand off and it will drop you like a rock. You use your hand as friction, as well as to place more rope pressure on the descender to enact more braking. With a standard descender you must manually put it into braking mode, or lock off. A good setup allows you both a soft lock and a hardlock, at an instant, on or off, left or right hand and without even looking As a tree climber, you live in the middle world between soft lock and hard lock with ascent and descent at either end and this is what allows us access to the outermost reaches of a tree canopy.
Friction control at this
easily achievable level allows us to do what we do well, which is
move around tree canopies mostly, and work-position for the moments when we rig and cut, or cable or do brace work.
Dependable, consistent, predictable, precise secure control of your rope on a metal piece is not difficult to perform. It is, in fact, so easy that you should be able to control your entire range of movements aloft with only a thumb and finger. Your whole hand gets to manage the rope, however, because that's just what we do. The piece takes on almost all friction. Drop it into soft lock, you can hang suspended. Drop it into hard lock, you hang suspended, bombproof, and you're able to turn away, manage your flipline, saws, rigging, etc. Getting in and out of soft and hardlock is something you do somethimes hundreds of times a day working a big crown. How well a descender does all this is the mark of how useful it is, how well it allows you to climb for a living. if 100% of your income is derived from tree climbing, pruning and takedowns, how well you handle friction will have a profound effect on your paycheck. You control friction for a living. That ability is the foundation for confident and safe tree climbing. That's why we as tree climbers take it so seriously.
Does this help?