My mechanism slightly different from yours , can't make out how your door pivots open but probably not to dissimilar from mine.
When I had an issue with mine I used a couple of metal rods located in the holes as per photo and a spanner on the adjacent nut and basically wound the spring loaded...
If you are confident with your soldering skills then crack on a pipe bender is an expensive bit of kit just for a one off (or 2 or 3 occasions), as a DIYer I have soldered joints under floorboards, in the ceiling and behind replastered walls and have not had any issues in 40 years. I have some...
Short on facts, but c16 5 x 2 spaced at 400 centres satisfies structural requirements for a standard floor load of 150kg/m2 so depending how your SE is adding on the weight of the bath the 150 x 50 could be in the right field if he means to replace the existing joists, if he means in addition...
Can you take a longer shot of the bar leading into the pulley (to ascertain whether there are any sprocket holes as per the video example and/or nut for spanner connection) if so we can take it from there? If not then its a case of mole grips and lap of Gods
Not 100% but if you can prise off end plate you may be able to do some adjustments. My thought is if you can move the door out at the bottom and middle hinges it may swing the bottom leading edge of the door more upwards when opening and not catch the carpet. Not certain on that but perhaps...
The supports at each end look OK. If SE says upgrade to 150 x 50 I assume he is discounting any assistance given from the existing joists and in theory these could be taken out altogether??? Obviously leaving them in will give you a stronger floor but trying to sister the new joists to the old...
I remember my history teacher saying in the 1960s it's not the power they hold but the power they prevent others from holding, perhaps he foresaw the likes of TACO??