You need to make space for a dog in your life -- you can't expect it to fit into various disconnected niches. Sorry.
Dogs are social animals and do not like being on their own. The reason dogs are so happy when you return from work\shopping\going outside the door, is due to them believing when you leave, you will have left forever.... every time you leave, you will upset it.
6 hours a day is a long time in the day of a dog.
a dog that wants to run will need to be kept fit, and will not be a dog that will want to be left alone and may be destructive through frustration. An Oxymoron.
an older rescue dog may come with its own personality flaws or 'damaged'. Many years ago I had a pair of dogs that were rescued. One was a Samoyed and the other a German Shepherd. I knew it was a big ask to take them on as a pair, but in those days it suited my way of life.
Both dogs were beaten as pups. The Samoyed had a real Jekyll and Hyde. A lovely dog (as many are) that turned nasty if you went within 10 feet of its feed bowl. Also as hairy as hell.
The German Shepherd was very timid and was a lovely dog. She gave birth at 11 months old (who was impregnated by the Samoyed), and gave birth to a pair of pure white germen shepherds and some black dogs with curly tails. The Samoyed had to go as he would go for visitors and bit me a couple of times (warnings not savage), but the GS became a lovely dog but took a lot of work... but she was worth it!
For allergies, a dog that does not moult has the best chance. We have a Bedlington who does not moult although sensitive visitors still suffer.
Washing a dog is not good for its coat as it washes away oils, but without washing skin flakes can be the allergen.
A four year old dog is a third to half its way through life. basic training starts at 11 months, with more serious training around a year and a half.
Most of the rest of the items is training. If you want most of your ideals, you will need to put a huge amount of training in, including fitness training.
Some of the other items are personality traits\flaws... '8)' as dogs naturally do many of these things with some breeds more than others. You stand better chance with a bitch as some of these traits are dogs trying to become 'Alpha'
My father who used to judge and show at crufts taught me loads about training. He ended up in Canada training and teaching the Mounties for search and rescue. GSD's could walk\run behind horses for many miles in a day, every day, but were super fit and had to run every day to maintain fitness.... their lives were much shorter than pets. A large amount of exercise wears joints quickly. Unlike people, many dogs are destroyed or pensioned off when their joints go... (a super fit dog often cannot mentally cope when their joints go)
Like people, not all were suited to fitness training and many were rejected to find suitable dogs (you cannot really trial and error with pets!)
if you really want a dog, you will need to reduce your requirements list somewhat.
