I have been reading all your posts.Aiming for putting the house on the market by 1 Feb is reasonable and achievable, I have cleared by father in law's house and my own dad's. Obviously you have the added emotional element of it being your home and having to look for another but it is likely that it may take a while to sell as the stamp duty holiday finishes in March which has attracted sales, so you only have to have the house 'view ready' you can continue to sort and clear during the selling process and a final push as you near exchange towards completion. Hopefully if you get a quick sale and have found a property in the New Year you may be able to move some of your things there as you sort. Anything your brothers and you agree that they should have, they should take at each sorting.
It may seem daunting for you but if you are methodical. determined and focussed you will be surprised how quickly you can get it done even with your teaching job. It is annoying that the brothers may not help much, I have been in that situation, but just let it all go over your head, be concerned only with the things you can influence or change...just keep the end goal in view.
Your brothers will not change and it is not helpful for you to keep worrying about what has been said or how little they have done in the past, I speak from a situation with 2 sisters where dad's care, decisions and house were left to me to sort. From now on be assertive and civil. don't give them opportunity to rake over their thoughts about you or the past...your care for dad, decisions or anything... when they visit or email, let the brother look for houses for you if he wants, you don't have to take up his suggestions but you do need to start looking and viewing for yourself...online initially if necessary during this time. It strikes me from all your posts that your brothers have a direct and blunt manner which lacks expression of empathy and if they have always been like that to you, doubt they will or want to change. Time to take a deep breath and look forward to having your own place with no interference.