How can I make these cookies less sweet without ruining the texture?

As I'm sure you know, sugar has many functions in baked goods, so replacing it can be tricky. Syrups will make your cookies too moist and just reducing the sugar can change the texture and browning. Sugar alcohols can add sweetness, but they usually don't brown and they can give people "digestive issues". I think your best route will be replace at least some of the sugar in your recipe with a different type of sugar, while keeping the total amount of sugar the same.

I think your best resource may be a brewing supply store, as they often sell other types of sugar to help control fermentation in beer. Brewing sugar, also called corn sugar, will be easiest to find and it's almost entirely glucose. In your case, granulated glucose will have the advantage of only being about 70-80% as sweet as sucrose. If this reduces the sweetness too much, you can try blending the granulated glucose with regular sugar. There are other sugars that are even less sweet, like maltose or lactose, that could be used to replace some of the regular sugar in the recipe, but they can be harder to find.

For reference, here is a chart of the relative sweetness of various sugars and sweeteners.

On second thought, I wanted to add some more information beyond my comment, so here's an "answer" and/or a continuation of the conversation...

As for my first thought: substitute something else for some or all of the table sugar: There are a pantload of different sugar-alternatives on the commercial market today -- some naturalish like sugar alcohols (erythritol, xylitol, ...), Stevia extractives, etc. Some not-so-naturalish (sucralose, saccharin, aspartame, acesulfame potassium). Some of these have alternatives with fillers that allegedly measure volume-for-volume as table sugar.

• Sugar alcohols like xylitol and erythritol (and to a lesser extent, sorbitol, maltitol, isomalt, ...) have relative sweetnesses of something like 60%-80% that of sugar, so could be an alternative if you'd like ~1/3 less sweet cookies. Xylitol and Erythritol have commercially available packages and can be measured volume-for-volume in place of sugar, according to some. Searching a bit for cookie baking results of wholly substituted (e.g., 1C xylitol in place of 1C sugar) yields some disastrous pictures (e.g., the ones with non-sugar only don't yield a result that looks like the cookie you're seeking). Consider substituting part (e.g., half of the volume) of the sugar to start. I've used xylitol, erythritol, and isomalt in various situations with reasonable success, but never in something sweet and delicate like cookies. Note, though: consumption of large quantities of sugar alcohols will result in exactly zero intoxication, but potentially non-zero bowel discomfort and related side-effects. Caveat emptor.
• Sucralose and stevia have commercial formulations (i.e., mixed with various fillers) to make them measure like sugar. I find the actual taste and mouthfeel of both of these to be intolerable, but it is nonetheless an alternative for some.
• Other (actual) sugars such as turbinado sugar, brown sugar, or even light molasses may have (to you) a less sweet taste that you might accept.

Have you tried simply using less sugar with no other modifications? Apologize if I missed this in your description above. I also must submit that you might consider a cookie other than a sugar cookie if you don't like the sweetness. Have you had snickerdoodles whose sweetness is acceptable? Gingerbread cookie, molasses cookie, peanut butter cookie, oatmeal raisin cookie, etc. I have done this (reduced sugar, along with reduction of baking temperature/time) with some success when making chewy ginger cookies.

As for flour substitutions, you might consider using some higher-protein flour (e.g., "bread flour") in place of some of the AP flour; this could make your cookies more chewy, but perhaps in a different way.

With a few dozen batches, perhaps you'll be able to perfect this by the New Year when belt-tightening resumes...

Edit: links to relative sweetness guides; search for more...

• From Oregon State: http://food.oregonstate.edu/learn/faq/faq_sugar53.html
• From Some Other Website: http://www.sugar-and-sweetener-guide.com/sweetener-values.html

Xylitol is approximately the same as sucrose. Erythritol is about 65% as sweet. Glucose is about 75-80%. I.e., these are less sweet or as sweet as sucrose.

Based on that, I'd recommend trying glucose powder in place of your sucrose.