When to put into hospice?

At 92 with obesity and with a swallow problem, I think that might be a good option, and certain a good option for palliative care. There is generally a two week period in which you can tell whether or not a stroke was a "small one" and the patient may recover swallow and all other deficits. If these deficits are there after that a good recovery is unlikely. Food could be deadly with aspiration pneumonia into the lungs. Tube feedings would be nonsense, cause diarrhea and pressure sores esp in the obese or the emaciated. I would support whatever decision the POA and doctors seem to feel might be best, were I you.

It's not just the stroke that's at play here making hospice a viable option. She has dementia and cannot walk, has swallowing issues which is a HUGE problem in and of itself and often leads to ongoing aspiration pneumonia, and is obese. Just the swallowing issue ALONE is enough to qualify your godmother for hospice as that is a very serious problem. At some point, a 92 year old body cannot 'recover' from all the issues that are present, and comfort care is the right answer. Hospice doesn't mean she's going to die immediately............just that no heroic actions are going to take place to keep her alive longer, in this debilitated condition. She can go on for a year or more in Hospice care, nobody knows for sure.

Her doctor will review her health history to date and if he feels that she has 6 months or less to live, he will recommend hospice. You can fire hospice at any time, don't forget, and take her back to the hospital for life saving medical treatment if you feel like you want to, or, you can choose to keep her comfortable until it's time for her to pass. I had hospice services in for my dad and it was a good all around experience.

Wishing you all the best at this difficult time

The number one comment I read about hospice is that people wish they had started sooner. Hospice shouldn't be a decision about hastening death, it is supposed to be an acknowledgement that pursuing treatment isn't going to change any outcomes and may in fact be detrimental to her quality of life.
We don't have Hospice per se where I live in Canada but my mom was considered palliative for many years before she died. What that got us was a greater level of services in the home including visits from a palliative care nurse and also home visits from mom's doctor. Although the doctor also greatly reduced (but didn't completely eliminate) the amount of meds she was taking my fears that she would immediately stroke out and die were unfounded, (although in retrospect that might have been a good thing).