I still think you are being very hard on yourself - you are dealing with a tough situation many people would struggle with.

I think Eskie makes a wonderful point, you can still spend that time with him when he is in a care facility. A wife of a man who went into a care facility once told me she had struggled with the decision but realised she had made the right choice when she was no longer exhausted from caring from him - she found she could enjoy simple time with him, playing games together at the care facility which she was too tired to do before. She is still a care giver, just on her terms, and the stress has been lifted from her.

I understand that the choice of facilities may be poor where you are but running yourself into the ground is not an option. Everyone has their limit and it sounds like yours is giving signs it's up.