I have only had Fridges WITH ice makers and water dispensers for the past 22 years.
Both are Kenmore one was a Kenmore/Whirlpool 29cu.ft (owned for 19 years without a single problem, sold for $350) and the one we have now is a Kenmore Elite/Samsung, (almost 3 years now without a single problem)

Have never once had any problems of any kind with ice/water.

The only thing that I kind of regret at this point is buying CD, while it looks WAY better in our small kitchen the depth of the drawers and overall lack of space even in this 24cu.ft model we have is disappointing when used to our huge fridge for so many years.

When we sell this house will probably sell fridge with it, and will NOT be buying another CD fridge in the future UNLESS I can have a second fridge in the garage or something like that.
The fridge itself is very nice, quiet, works great its just the size of a CD fridge no matter which one is just plain lacking.

You're right. Not many options in a non-dispensing CD SxS 36" fridge. Especially in the non-high end market. I haven't heard the best things about Northland fridges so would be hesitant to go there. Don't know about DCS other than their cooktops and ovens.

I was going to suggest a model with internal water and forgo the water hookup, but that doesn't open up any more choices really.

Have you used a bottom freezer model at all? I used a French door (can't stand FD myself for the fridge top) and now have a single door fridge with bottom freezer. There are units with freezer organization systems that prevent a messy freezer. Besides the ice maker, mine has an internal upper drawer and three bottom compartments, two small and one large. I don't find I lose anything in mine, but generally in the main compartment items are stacked two deep. Not a problem at all for me as I store meats and fish on the bottom and only use those at most once a day. I love opening up the full-width fridge door and not having to stoop/bend over for anything. Just a thought for you and I opens up dozens more options for you.

Here is a link that might be useful: Ajmadison's list for your requirements

Just because it has a dispenser or ice maker doesn't mean you have to hook it up. And with that in mind, look for one where everything is in the door. This takes up less space.

We bought a counter-depth (I assume you mean a fridge that does not jut out past the counter top) side-by-side roughly ten or twelve years ago. It is an Amana, was special order, and we've had no problems (yet) with the ice maker or ice/water dispenser. You always have the option to not connect them to the water supply. I don't know if Amana still makes this model fridge.