Really struggling with cleaning/ household tasks

Hmm, yes; I have rather a problem with this myself - I find it hard enough to keep my person clean and tidy, never mind my home.

As suggested in the OP, it's certainly an attentional problem at some level. The people who I share my computer programs with always comment on how meticulously neat and tidy they are - I wouldn't dream of uploading something with graphics that look skewed by so much as one pixel, or lining up all of the "=" signs in the code. I was once nicknamed "Midas" by a supervisor because I could never resist "gold-plating" everything, and writing a couple of paragraphs for a forum post can  take me an hour or two sometimes, by the time I've obsessed about every single word (or rather, I write fifty paragraphs, then struggle to edit down - hence my rather TL;DR posts quite often).

Meanwhile, I could have a bag of rubbish that needs putting out in the middle of the kitchen floor that I'll step around for weeks, apparently not conscious of the inconvenience or even the existence of the thing (until  I trip over it and it bursts, followed by the inevitable melt-down!). If archaeologists carefully chipped away at the brown encrustation sat next to my computer, I might rediscover what made my favourite coffee mug so appealing!

Lists don't work for me at all; they just end up becoming a focus for procrastination, and I have really bad completion anxiety, so I don't feel like I can start until I have a detailed plan for acheiving everything on the list - and I'm never satisfied with the plan, so I just tinker with it until I give up because the list is just a mess of arrows and crossings-out.

Favours required by other people are never anything like such a problem as self-directed tasks - I'll happily visit a friend to have a go at fixing their washing machine even when mine's been broken for months (there's never a "round tuit" in my toolbox!) It removes the element of "deciding", which is far more of a problem for me than the "doing". I've been noticeably better since I moved into a bedsit with the landlady living downstairs; I even do all the hoovering because she has a disability which prevents her from doing it herself.

Something that I have found works quite well is to make use of the ubiquitous camera-phone. Rather than writing lists, I take a picture of the offending mess, and put it up on my PC somewhere that I'm bound to notice it (the desktop background even). Besides the reminder, it really helps me to feel like I've achieved something if I can directly compare before and after - it makes what I've done seem more "real" somehow, even if the "after" is still not as tidy as I would really like.

I also use my PC's calendar a lot, too. For example; I get a notification every Thursday that it's bin-day tomorrow, and try not to let mysef dismiss it until I've completed the task. Rather than a long list, I get presented with just one thing to do right now, which is much less overwhelming. The "do anything rather than nothing" tactic can work quite well too, sometimes - if I find myself procrastinating about which task to do out of a list, I'll choose one completely at random to take away the decision making part of the problem (I have a little computer script that I often use, but dice or pointing without looking would do just as well, I guess).

The most frustrating part, I find, is that I just don't seem able to describe this problem to anyone in a way that they'll understand. Social services etc. just don't get why I need help with it; the usual response is to suggest that I'm depressed, or at most, to offer remedial lessons in the practicalities of how to clean things. You would think that with more awareness of ADHD, Alzheimer's, etc. these days that they wouldn't be quite so clueless.

Hmm, yes; I have rather a problem with this myself - I find it hard enough to keep my person clean and tidy, never mind my home.

As suggested in the OP, it's certainly an attentional problem at some level. The people who I share my computer programs with always comment on how meticulously neat and tidy they are - I wouldn't dream of uploading something with graphics that look skewed by so much as one pixel, or lining up all of the "=" signs in the code. I was once nicknamed "Midas" by a supervisor because I could never resist "gold-plating" everything, and writing a couple of paragraphs for a forum post can  take me an hour or two sometimes, by the time I've obsessed about every single word (or rather, I write fifty paragraphs, then struggle to edit down - hence my rather TL;DR posts quite often).

Meanwhile, I could have a bag of rubbish that needs putting out in the middle of the kitchen floor that I'll step around for weeks, apparently not conscious of the inconvenience or even the existence of the thing (until  I trip over it and it bursts, followed by the inevitable melt-down!). If archaeologists carefully chipped away at the brown encrustation sat next to my computer, I might rediscover what made my favourite coffee mug so appealing!

Lists don't work for me at all; they just end up becoming a focus for procrastination, and I have really bad completion anxiety, so I don't feel like I can start until I have a detailed plan for acheiving everything on the list - and I'm never satisfied with the plan, so I just tinker with it until I give up because the list is just a mess of arrows and crossings-out.

Favours required by other people are never anything like such a problem as self-directed tasks - I'll happily visit a friend to have a go at fixing their washing machine even when mine's been broken for months (there's never a "round tuit" in my toolbox!) It removes the element of "deciding", which is far more of a problem for me than the "doing". I've been noticeably better since I moved into a bedsit with the landlady living downstairs; I even do all the hoovering because she has a disability which prevents her from doing it herself.

Something that I have found works quite well is to make use of the ubiquitous camera-phone. Rather than writing lists, I take a picture of the offending mess, and put it up on my PC somewhere that I'm bound to notice it (the desktop background even). Besides the reminder, it really helps me to feel like I've achieved something if I can directly compare before and after - it makes what I've done seem more "real" somehow, even if the "after" is still not as tidy as I would really like.

I also use my PC's calendar a lot, too. For example; I get a notification every Thursday that it's bin-day tomorrow, and try not to let mysef dismiss it until I've completed the task. Rather than a long list, I get presented with just one thing to do right now, which is much less overwhelming. The "do anything rather than nothing" tactic can work quite well too, sometimes - if I find myself procrastinating about which task to do out of a list, I'll choose one completely at random to take away the decision making part of the problem (I have a little computer script that I often use, but dice or pointing without looking would do just as well, I guess).

The most frustrating part, I find, is that I just don't seem able to describe this problem to anyone in a way that they'll understand. Social services etc. just don't get why I need help with it; the usual response is to suggest that I'm depressed, or at most, to offer remedial lessons in the practicalities of how to clean things. You would think that with more awareness of ADHD, Alzheimer's, etc. these days that they wouldn't be quite so clueless.

I have exactly this problem, explaining it to anyone is seemingly impossible. Going to try some of these suggestions and see if they work for me.

I often think I need an autistic neighbour, I would pop in and clean their house and they would do mine.

There's something about being able to enter and leave.. And be objective and unemotional about what I'm cleaning.. that I can't apply to my own home. 

Thanks for reminding me to put the bins out, LOL! Yes never like a big list, one small step at a time.