I can do so in my oven and I am cooking in an original to our house. . .
Gaffers and Sattler oven, installed circa 1970.
Do not have any problems with over-browning of cookie bottoms. I use quarter-sheet size fairly heavy aluminum baking sheets with edges that go up about 3/4 inch (jelly roll pans?). And because the pans are staggered side to side I do need to move the pans from side to side and spin them front to back, especially when cooking with multiple pans, and of course everything takes just a bit longer as the oven door is open more.
Always toyed with the idea of getting some of those insulated cookie sheets, but was too cheap to fork over the money for them as my oven cooks pretty dang good.
I do have a very heavy high-fired ceramic bread stone in the bottom of my oven that resides there 24/7. I think it helps to even out the oven heat and I can get great bread and pizza off of it.
Have you had your oven thermometer checked? A long time ago we had ours checked and the service guy said that it was not uncommon for those things to be 50 or more degrees off.
You might want to try using a good oven thermometer to see what you oven is actually cooking at.