I was hoping someone would answer your post cause it is kind of interesting. Perhaps it is because you have laid a lot of requirements on simple grass. I'm not sure there is one type that meets all of your desires. You may want to research the hybrid bluegrasses though some say the newer elite varieties of KBG are just as heat tolerant. Mixed with tall fescue appears to be popular with sod producers in the more southern parts of the transition zone. Overseeding bermuda with rye is a traditional southern golf course technique for green winter cover, but is expensive and can be hard on the bermuda. What level of maintenance, cost, and effort are you willing to go to to achieve your desires? The shepherds will wear out the grass if left in a small space. There is no grass that can tolerate that kind of wear without intensive maintenance. You may want to find out what grass is used on football and soccer fields in your area. Chances are that will be the most wear resistant. How do you intend to maintain the turf?

Do you even have summer? Don't y'all head for Aberdeen when you get 3 days in a row above 20 C (in the 70s)? For summer feeding it is better to use an organic fertilizer. I like alfalfa pellets (rabbit chow) at a rate of 10 kilos per 100 square meters. I get alfalfa at feed stores. Here are the feed stores near you. I use alfalfa because it is inexpensive in my neighborhood. You can use any ground up nut, bean, seed, or grain. I'm not sure what you can get in your area, but I'm pretty sure people raise rabbits everywhere. A side benefit of the organic will be that you should never see a dog spot again. That is a dog spot. It might not be from the fortnightly dog, but that's like a poster child image of a dog spot. Classic! On a more immediate basis, what I do is scatter a heaping handful of sugar on the spot. The sugar kick starts the soil microbes into the re-population mode. They will quickly grow in numbers to a point where they can deal with the sudden appearance of urine in the soil. In about a fortnight and a half you'll see that spot growing much faster and greener than the rest of the lawn. I think you're the first person on this forum who has admitted to properly fertilizing with a liquid fertilizer. If you are going to use liquid, it has to be done every half-fortnight. In our American heat we can't do that in the summer, so granular is the way to go. That way we can apply about 3 times per year and not deal with liquids every half fortnight. And yes, I'm trying to figure out every way I can to use fortnight instead of Imperial time units. ;-)

Soil test. It's pretty late in the year (or early, I guess) to be feeding. The grass simply isn't that hungry in January. +1 Boat. Don't blindly throw resources at the soil (nitrogen being an exception, always target the grass' preferred amount of N per year without consideration of any other resource). Testing can be thrown off by application of some things, but a high nitrogen fertilizer is safe. Even if the place you choose (like UMass) tests nitrogen, we ignore it. It varies by moisture level, soil temperature, and time of day--and the actual number doesn't matter.

While supplementation with any fast nitrogen source would work (whether it's urea, an ammonium or nitrate source, doesn't really matter), it could come at a cost. Better fed lawns will respond to still more nitrogen arriving in the dog urine by burning (that tendency will also increase as temperatures rise and the soil gets a bit drier). You may need to step up the amount (or frequency, depending on your schedule) of feeding you're currently using for best results, but you'd have to let us know what that is.