On the sling subject - a Tomy or Baby Bjorn kill you after the baby gets to this sort of age, but a soft structured carrier (Boba, Ergo, Maduca etc) are designed to make it easy - you can do a back carry, and a lot of the weight is on your hips due to the design. I'd investigate that if you have a velcro baby. I could carry mine until DS was almost 4 in one without that being a problem at all, and he was huge for age (still is).
Weaning foods - if you're spending hours making them, maybe investigate baby-led weaning? As long as you eat homemade food rather than ready meals most of the time, it's massively less faff and not in any way bad for the baby - in fact there are arguments that it's better for them. No baby needs purees at 7 months, anyway; we assume they do because we used to wean at 3 months or so, when that was all a baby could handle. That might free you up a bit? Even if you go to a coffee shop and watch the world go by, I find that a lot easier than being stuck indoors anyway. And it's fun for the baby, people-watching.
I'm afraid I also agree that a jumperoo is horribly noisy in a wooden-floored flat, and the 7 am one is really selfish I'm afraid. It's hard managing a baby in a flat - I know, as I've done it - but you can only make it work if you try to think about what you can do to ease a baby for them, as even when you do do that to the absolute best of your ability, there will be irritations they have to swallow. Does the neighbour work? Maybe restrict the jumperoo when you know s/he's out? If you ask them to let you know their routine so you can accommodate it, then you're showing willing which will also help you if they go to formal complaint level.
I sympathise on the screaming colic front though. DD is a huge screamer and I am mortified for our neighbours, but there is genuinely nothing we can do - all our bedrooms border a neighbour's, as we live in a terrace. I used to take her downstairs on especially awful nights but that isn't an option available to you.
If you can afford somewhere with a garden, then that's massively helpful as a parent anyway as the baby gets older, and would eliminate the neighbour issue. Maybe start to have a look around to see what else there is? Spats with neighbours are miserable for everyone.