Sounds to me is that the only reason you were "pondering" the idea of him being your "house husband" is because Mr. Handsome&Charming-But-With-Neither-Integrity-Nor-Shame has been pressing the point somewhat. So keep these two things you've said at the front of your mind whenever he's with you -
. "He has tried to trample on my boundaries before a few times."
. "He can be quite determined at times when it comes to trying to overstay his welcome"
Basically, he wants a better gaff than his long-suffering parents provide (I wonder if they've been hinting it's time for him to leave). He's targeting you to provide said better gaff. He plants the notion of 'househusband' as a possible solution to you being "run ragged" and hopes that you are both enamoured with his penis AND are run ragged enough to overlook his propensity to take to his bed with "putting on a stupid voice and limping around in his robe for no good reason" whenever he is "exhausted".
Dear God, he's a wearer of The Dressing Gown of Doom! (you'll find many threads on Mumsnet about the DGofD.)
Also, you've said:
"He doesn't have a very stressful job, he just doesn't seem to be able to handle ANY stress at all. Things need to run smoothly for him at all times."
Because there's no stress in running a household that involves children, none at all, no sirr-ee! Such a household runs smoothly at all times. No lost PE kit, no sudden and inexplicable food dislikes, no squabbles over the TV remote, nothing. Smooth, smooth stress-free household. Which will run itself, smoothly and stress-freely, whilst he takes to his bed for a couple of weeks. Uh-huh.
I'd actually use that against him, personally. - 'No Derek, you'd be useless as a househusband, you'd be taking to your bed with the stress of organising and decluttering the house and looking for little Jonnie's PE kit and frankly I cannot be arsed. Your whole life revolves around 'stress' and avoiding it, which just exports the stress to those around you and I am not willing to deal with that, your cock isn't THAT good, you know! I'll let you know if I'm ever in the market for an exotic pet, but know now that's very unlikely to ever happen.'
One thing that occurred to me, about him currently being on "long term sick leave and who probably won't work again by choice". You said it's "Stress leave. Unable to cope with workplace stress after a reshuffle."
'After a reshuffle'. So, he didn't like his new job in the company. Was it a step up, or sideways, or downwards? I ask because although my first assumption was that the reshuffle was to a higher-stress job, all the things you've posted have made me wonder - really, really, wonder - is his long-term sick leave actually just a massive sulk? He didn't get to be where he felt entitled to be so her flounced off with 'stress' (notoriously hard to disprove since everybody's different) and being a "lazy git" lacking in integrity found that his flounce suited him just fine.