It doesn't change my prior advice by much, but I would just reiterate that their current offer is just the opening gambit.
By mentioning a bit more of the history of it, you've just confirmed to me that they will definitely be willing to go much higher.
They are obviously acknowledging that they need to lose one person from your team and they want that to be you for "political" reasons. They will not want to have to use a redundancy route to get rid of someone else, so you may find that their pockets are very deep on this one...
The poster below me originally said that, as HR, they usually offer 1/3rd of what they're actually willing to pay, as a guideline.
You can always counteract with, say, 5 times what they're offering, then negotiate to a middle point.
What you then do with that money is up to you. If you get a new job quickly, then have a decent holiday or stick it in a pension, or give it to a charity that helps people that have suffered SA.
On that last point, I hope you're OK, given what has brought you to this point.