Did you want blue flowers? Got that impression, since all of these come in at least blue, if not other colors also. If blue is not an overriding factor, I'd lean towards the hydrangea (it's pink and a pretty stable pink at that), as it's the right size and would prefer a part/morning sun location. And I'd opt for the veronica before the rosemary - veronicas come in a wide range of heights and they are very showy when in bloom. Rosemary can get BIG (where sufficiently hardy) and would be happiest in full, all day sun. May not like your summer humidity much, either.

I have one in the front yard. Its in a mostly sunny spot, decent soil (not too sandy, not too rich) with some hardy cactus, russian sage and salvias. Mine doubled in size last year (first year) and I know it bloomed for a little bit at one point but I honestly can't say I remember the color. I remember reading, too, that it could be white or it could be a blue/lilac color. Having said that, I don't think its really grown for the flowers - I chose it because its low-growing habits and color (you're absolutely right - this with a dark purple ajuga would be beautiful! Like I said, mine is with the dark purples of salvia and light blues of russian sage but a deep, almost black purple would be beautiful with this!). I'm right on the border of zone 5 and 6 in Michigan. I'm sure I don't need to tell you what a crazy winter we had and, even though snow insulates, we still had a few weeks for -10ð and my creeping sunshine made it through. Never dragged a hose across mine, and its still quite small, but it seems to be very dense and matted so I would imagine, after a little maturing, it would be able to stand up against a hose. If you already have them give them a try and if they don't work out then I have some false lamium I can send you... talk about a resilient ground cover (JUST KIDDING lol)

Fried, in this extreme heat? Mine do the same thing every year for the most part. Then they bounce back in spring and look fantastic (or even in winter here they look good). This year in particular due to high heat I've had many plants look terrible and and some have gone dormant.

Directions for adding zone and location info: Go to Your Houzz in the upper right of every page, click Edit Profile, and on the left side click advanced settings. Well down the advanced settings page is a blank labeled Climate Zone for Garden Forums along with a link to find your zone. If you add info on your state or the nearest large city you will get even better information since zone only relates to average coldest winter temperatures and can vary over a wide range of other factors. Then return to the top of the page and click Done Editing.