I can't tell you how to beat avolition because it pretty much controls my life, but I have a few tricks that I try to use regularly. You already mentioned scheduling. Planning the chores I'm going to do and then crossing them out when I'm done makes it easier to do more and to keep track of when you're doing it right and when you didn't quite make it work. Another tactic I use when I feel tired is to just get up and
start doing something. It doesn't have to be a lot, doesn't have to get you anywhere or even be useful. And it's OK to just sit down again after ten seconds. But getting up and starting an action makes it so much easier to actually finish it. And it's not very tiresome when you know you don't have to do anything more than you want to. My third tactic that I am trying to start using more is helpful lists. I have one list for morning routines (before I made that one I didn't even have morning routines - i.e. no brushing teeth, no eating, no nothing. That one list has helped a lot even though it's deceivingly simple), one list for long-term goals so I don't forget about them (just regular stuff like sending a letter, scheduling an appointment with a dentist, etc), one list for helpful things to do when I'm feeling bad, and one list that I've just tried once yet, but it seems to be helping a little, where I write down the things that are bothering me so I don't have to keep thinking about them to remember them.
Hope this helps someone and also hope I can learn something from this thread.
Also, don't give up. It's OK to give in when everything is too much to deal with, but go back to trying your best again when you're ready. Setbacks do not equal defeat. I'm still going to start working out, even though I've been telling myself that almost every day the last three months since my last workout session. I made it work for two months though, and it did help me, so working out = good and I will start again when I'm ready.