Thin Cookies

One other recipe adjustment you could try: Adding a little extra flour.

The major problem in that is baking powder. People tend to keep baking powder in the cabinet far too long.
Get fresh...it's one of those items you just have to toss occasionally if it's been there a year or so opened. Check the expiration date--and consider that as the un-opened date.
I never go through a canister in a year and it decreases in leavening power over time.

I think these are all great answers. You might also consider using vegetable shortening in place of some of the butter--it spreads less.

I happen to have a left over egg white in the fridge right now and I was afraid it would get wasted! Thanks so much. I am mixing it with the remaining dough now and then I will let it chill.

My guess is you're getting pulses of too much heat in that relatively small box. There may be a solution, or a partial solution, in beginning with very cold or frozen dough.

You can try any of the following:

Decrease the sugar. Sugar becomes fluid when heated and makes cookies spread.

Add an extra egg (or egg white). The white will cause the cookies to puff and dry out.

Increase the leavening agent a tiny bit.

I would argue that it's most likely your recipes, not your toaster oven, that is giving you these results, though you may also have problems because the heat is harder to regulate in such a small oven. Have you tried cooking something that's innately pretty chewy, like a thumbprint butter cookie, and still struggled? You may also need to adjust your temperature (probably up) and your cooking times.

I have baked extensively in a very weird, tiny oven -- more or less a small metal box that sits right on top of a gas stovetop. For that, I have to be very careful about heat loss when the door is opened, so I jack up the heat substantially when opening the door, then turn it down again once everything is inside. I also find that a blast of higher heat followed by lower temps prevents undue spreading or butter leakage in chewy cookies.

My guess is your toaster oven runs little hot. If it has a temperature control try turning it down 25 degrees? Another suggestion would be to chill the dough and roll into balls but do not flatten. The dough should spread less.