It's recently come out that, on September 10th, Lauren Boebert was removed from the play Beetlejuice in Denver. This would be all fine and good, right? A politician is being an asshole. The sky is blue. Well, Hexbear, it is anything but fine. Anything but.
The plot thickens when it's revealed that, beyond the vaping and the being loud (which is it's own struggle session whether that's based), that part of her contribution to getting owned was that she was giving her partner an over the pants handjob. Now, this would have gone through the news cycle with a sensible chuckle for me, but, my fellow hexbearians, do I look like I'm having a sensible chuckle? NO! This is literally me right now.
See, what had happened was that this news circulated to the website that I like to post on. The title of the post was "boebert was giving a no-foolin for-reals handjob during the beetlejuice musical" This post got some of the most vile, vitriolic comments I've ever seen in all my posting.
>no-foolin for-reals handjob >over the pants rubbin Y'all that's not even a handy to a seventh grader. @regul@hexbear.net
unironically 
@WoofWoof91@hexbear.net
Let's get one thing straight here, hexbear. Over the pants is a handjob. This is my central thesis. Let's start with the most obvious positive case. If you have sex with a condom, do you call it over-the-condom sex? Of course not! Protected sex, maybe, but you wouldn't call it not sex. Would you call a blowjob with a condom not a blowjob? Of course not! If you did that'd be annoying and weird. Let's try not to be annoying and weird. skin-to-skin contact with the genitals isn't a requirement for something to be called a job. Repeat it once more for the people in the back getting a handjob rn: skin-to-skin contact with the genitals isn't a requirement for something to be called a job. If home runs are so unambiguous, why is third base so "ambiguous?" Because of a single fringe case. If it wasn't for the existence of this fringe case, then there's be no argument about how getting your genitals stimulated works.
Fairies, monsters, and others that go bump in the night, let me introduce you to the water jet/bubbling system of a hot tub. Wikipedia defines a hot tub as "a large tub full of water used for hydrotherapy, relaxation or pleasure." Let's explore that last word, pleasure. Whom 
hasn't used a hot tub as it was meant to be used. I think this is where the friction comes from, the jet stream in a hot tub. Dissenters will say (like sniveling cowards) "b-b-but WDYMP, the hot tub isn't sentient, it can't give you a job!" Let's get one thing straight, if you had your hands over the edge of a hot tub and your partner was pushing your crotch into a jet stream, that would be a type of job. The solution, my compromise for the haters and losers, is what I would like to call the jetjob. It would be a normal jetjob if they're pushing you via hands on the buttox into a water jet, and a reverse jetjob if they're using their feet. It would be a backwards jetjob if your back is facing the water jet. This also expands the capacity for a combo jobs because your crotch is facing your partner. This would be the exciting introduction of the triple job if they're using a hand, their mouth, and the water jet. I propose that, upon climax in such a fashion, one would exclaim "Tic tac toe, three in a row!"
With this, let's get one thing clear, over the pants is a type of handjob the same way that over the condom sex is a type of sex. If we can start using the term jetjob, then it will be easier to recognize when something is a job and when something is not. This would also be a step closer to communism. Thank you. I hope I haven't fractured our fragile community too deeply with this.
Based off of this I think we can come to a full completion of the discourse at hand:
IF there is an intention to cause arousal of the genitals
AND there is contact with the genitals
AND anything occluding the genitals is malleable under the force of your partner's grip
THEN you are receiving a handjob
OTHERWISE it is a chastity cage and cannot be subject to any type of job
By this conclusion one may infer that the stronger the partner's grip strength, the more rigid the occluding sheath may be and still be capable of giving a handjob.
I agree with most of your reasoning except:
First off many chastity cages would meet the criteria you laid out (NSFW but just the cage), and secondly, I think it's possible to get a job while in chastity, for example, I think stepping on a caged cock could qualify as a footjob.
Just to add it to the mix, I'd also like to raise the question of whether using an intermediary object like a grabber could potentially qualify as a handjob.
I think we still need to distinguish between chastity cages and physical barriers, so I think calling it a "full completion of the discourse" was, in fact, premature.
I would be willing to compromise that if an object can be classified formally as a chastity cage then the crushing thereof would be considered CBT and not a hojo. But to that end I would define stepping on a caged cock CBT and not a fojo. And ergo cum loudly grabber hojos are still hojos ~~(if that's anyone, DM me)~~. What is a physical barrier besides a chastity cage if someone's intent is to arouse you?