Although I don't understand all the different services that the Seattle Animal Shelter offers (perhaps matched by the three different main entrances on different sides or levels of the building), I DO know that they offer a pet bereavement group.
This drop-in group meets for 90 minutes at 6:30 every Thursday evening, and I have gone there four or five times. Each meeting has a different facilitator/volunteer and allows the usually small group of 4-8 people time to share their experiences and come to terms with the death of a beloved pet. There is no fee, and registration is not required to attend, either.
For that alone, I am very grateful to the Seattle Animal Shelter.
It is unfortunate for the cats, as well as the volunteers that work with them, that the felines are housed in an area not that far removed from where the dogs are housed, as the yelping and barking is very loud and CAN be heard clearly, despite the steel doors.
The cats are housed in small--but large enough for them to get up and use the litter box or to eat--metal-bar cages with bar, stacked on top of each other in rows, in two different rooms (one for those with health issues). But they don't really have room to move around.
I was going to volunteer here (they have training sessions every 3-4 months) but the training was rather onerous for someone who only wanted to work with cats, as the first session was entirely devoted to dogs. And then there were several mandatory sessions--with no fixed schedule--and a one-year commitment ...too many hoops to jump through.
And then my 19-year-old cat needed me to care for him at home, anyway...
Other local pet shelters include: