Just wanted to provide an update on this. I bought the Vytronix hoover that
@Tia suggested and, to my great happiness, was able to easily carry it up the stairs in its box when it arrived. I just tucked the package under my arm! Very light.
I put it together easily and used it for ten minutes with no problem when it suddenly cut out, spewing dust from the floorhead, because of the sheer amount of dust it had pulled up from my small patch of carpet (hadn't been hoovered in nine months). It must have triggered a safety cut-out because it came back to life after I emptied the cannister and removed dust from the filter (both easy to do). Over the next few days I did the whole flat and pulled up a ton of dust.
I'd be curious to know whether my standard hoover would pull more up but I can't use it at all so I won't find out. But my nose has stopped running all the time and my eyes are less itchy.
I'm so pleased with this hoover! It really is amazingly light and usable.
Thanks again,
@Tia! And to everyone on the thread who pitched in with their thoughts.