A few things jump out from your post. I might well sound harsh (sorry!).
Do NOT do his washing. The home will do it and much better than you to be frank. Its not going to make a real difference to anything if you dont. The world isnt going fall in if home does it.
Dont take calls ooh. He sounds self absorbed and quite frankly like a lot of old people very very selfish. As others say this could go on for months.
Go a few times a week. No more. Be cheery and I found with my late Mum that if she started moaning I would literally say in a cheeful voice ' are you moaning again?'.
You will hear the following phases over and over again if you havent already:
'I dont want to be a burden'
'I want to die'
'The food isnt great and the staff arent good'
'You dont know what its like. I am at the end of my life'
Many many old people have NO idea how to deal with their old age, they have no plans so when they become old they panic. Cling onto whoever they can and literally wont let go.
My Late Mum also said if she couldnt contact me then who? Siblings lived abroad and were uesless.
I shut down any fancy ideas they had as to what I needed to do which normally involved me spending hours doing something.
So what if his suppoistry isnt here. What are you meant to do about it? Ask the nurses.
I think looking back its all attention seeking along with a side of feeling scared that the end of life is near (it might not be!). My Mum didnt make any plans for end of life. She apparently just wanted to fall asleep one night and not wake up.
The guilt is horrendous I know. I wasnt there when Mum died although I did see her in the care home after she passed which was OK. I am glad I did it. I am not going to say she looked at peace but it was her time.