Sincerely not trying to hijack your thread, and I know it's a year old, and I had no intention of posting anything about this, until I read the pain in your words. I'm hurting right now too so...
I lost my grandma a couple of weeks ago, she was in her 90's and lived a good long life. She put on a clinic on how to finish off your days, never complaining about anything even though she was near blind, 100% deaf in one ear and 80% in the other, unable to walk for the last couple of months etc. The day before she died she did say "why is this taking so long" and that's about as much of a complaint as she'd ever give. On the day she died she had a lot of trouble staying awake and her breathing could best be described as "inconsistent and sputtering" as if she was just too tired to breathe. She opened her eyes at one point and looked me right in the eye and said "I've lived a good life, love each other and treat each other well, I love you" and she fell back to sleep and passed on an hour later.
She had all of her mind and wits intact until the very end and that's more precious than anything.
Warning: even when you know that time is short and it's 100% natural without any pain... it hits you like a Mack truck for days. You are not prepared, no matter how prepared you think you might be. The permanent nature of it grips you hard. There was one of the worst blizzards in my state's history on the day I was born but she drove to the hospital to see me, she counted 18 cars in the ditch along the way and could not see more than 5-10 feet in front of her. I mention that because you only get a very small number of people in your life who would do that out of pure love and losing one hurts, a lot.
Take some time and spend it doing something with loved ones(yeah, cats count) because in the end everything else is trivial and unimportant in comparison.
disclaimer: this was written through blurry eyes, your story with Hammy is touching, we all eventually have to face a situation that is hard that way. Focus on the positive, remember the good, that's what they would want. I'm not even half way to 90 and realize that health comes in a close #2 to spending time with loved ones... take some time off the comp and get some exercise too!