I'd suggest Corian, but not if you want to cut directly on it. Unless you have butcher block, cutting on counters is not recommended either because of dulling your knives on hard surfaces.

We got Corian in the Rain Cloud pattern and they have others that are not "speckle"y. It is less hard than stone which means less noisy and less likely to shatter something dropped on it. It does not feel as cold as stone either to the touch. Our pattern does not show up every water drop or crumb, so that is easier than ones that need a full buffing after every use. It has a sheen but is not shiny.
It looks much different on a display than the sample and the website tiny pic looks nothing like it. I would google images of any pattern you like and try to see them installed. Luckily, we saw ours in a display kitchen and not as the swatch that they sent to us. We almost cancelled until we went back to the display and realized that it really was like the sample (which did not look pretty) but the tiny format did it no favors. The look is apples to oranges when you see it on a full counter.

You may want to look into honed granite or Cambria quartz. I believe they both have a matte type of finish. I believe the honed granite shows more fingerprints and smudges than Cambria but my knwledge of this is purely from this forum.

If you're going to cut on the surface, then don't do soapstone, even the hardest variety. However, if you're willing to be more diligent about not cutting, the it would look great. I chose soapstone for similar reasons such as not liking shiny and not liking speckled. I have a five year old, but she won't be five forever, so I didn't want to do something for today. Mine can be conditioned, but yours may be different. Only you would know how they'll handle the counter. If you kept some cutting boards or mats handy, it might not be to hard to condition. Even if you don't cut on it, banging milk bottles and utensils can cause surface damage. The good news is you can oil it out. Other than that, soapstone is beautiful and would probably look great in your kitchen. Some people mislabel soapstone as high maintenance. I prefer to consider it as high tolerance.

Well I guess Cambria is a brand of quartz countertop that you can get in a matte finish. So not all Cambria is matte.

If you'll cut on it, butcher block. Or laminate. ;) I occasionally cut a slice of apple or two on my old stuff, but I hated it and wanted to rip it out. Seriously, don't cut on the counters. Keep a large cutting board stationed near where you prep. As Dianalo mentioned, it's bad on your knives. It dulls them, which leads to more cuts on fingers because a dull knife is a dangerous knife.

Given your list, I recommend wood. Thought about that at all? Not shiny, usually not modern, can be rustic, casual, cozy, and not speckled. I have a black walnut island top. I LOVE it. I do not cut directly on it.

Thanks very much for the input! I had not thought about wood - will have to research that one some more :)

What about honed black granite? I've seen some pretty pictures of (I think) Absolute Black granite that was not shiny, but would probably look great, in a cottage style kitchen. I thought about it, but don't want quite that much contrast, with the creamy white cabinets.

I have honed soapstone. Maintenance is minimal, love it!

I think this would be a great case for the Brickmanhouse treatment. Wood countertops dyed flat black with India ink:

Here is a link that might be useful: India Ink countertops

honed granite might be a good option for you. benefits of granite that you have had before but honing removes the sheen you did not like.

I know you don't like shiny, thus may not have considered it, but stainless steel makes a wonderful rustic counter if it's got a brushed finish. Indestructible, period-correct for Craftsman, can't go wrong. :-)

Check out leathered granite...it doesn't show anything!! When we were building I was very tempted by this choice for my island since I chose a rather temperamental perimeter c-top...but true to my form over function nature, I ended up with walnut instead. Which would also be a nice, rustic choice for you, but it is not as bullet-proof as that leathered granite! Honed black granite is lovely and not shiny, but it still shows fingerprints. One of my friends has it.

Some really great ideas I had not thought of - honed and leathered granite -didn't even know such things existed. And I love, love, love brickmanhouse's kitchen. Very similar to our "look" with some different elements. My husband is not on board at all with wood counters though so will have to research and talk through that one but wow, I could save a ton on countertops with that option. If we had an island (not enough room) then I would definitely do wood at least there.

IMHO, granite is a great choice, there are so many color choices, i am sure u can find something that will work. you don't have to get a solid color. i got polished granite with alot of movement and it does not show any fingerprints. you have to bend down and look at level to see anything. and with granite with "movement" it doesnt show crumbs or really anything...that can be good and bad!!!

i am so happy with my choice. its really working for us in a great way.

best of luck, i know this is a tough decision!!