Bars come in various clamp diameters. Drops for vintage bikes ought to still be available which have the same diameter at the clamp as your stem, or you could change stems too. Measure the diameter of your current bar at the clamp.
Comfort, hybrid, and MTB bars ought to be 25.4mm at the clamp and 22.2mm away from the clamp. A set of drop bars for a vintage bike ought to be the same. Current road drops are 31.8/23.8mm so they are too big for your shifters AND you'd need a new stem.
There was an intermediate size with a 26mm clamp diameter but I don't know how big the rest of it was. These come in the modern shape which some find more comfortable.
You may not be able to get your shifters on around the curves in the bars especially if they are cast aluminum or magnesium (i.e. no chrome steel band holding them on), so you may be stuck putting them on the straight part on the very outside.
You could probably score some shift/brake levers from Ebay or new which would work with drop bars and let you shift without releasing the bars, just by pushing the brake lever sideways instead of backward. You'd have to find a set with the same number of speeds as your bike, as well as a cable clamp for your down tube. The levers are pricey, though.
If you have the funds, you could sell your bike and get a cyclocross bike. Those come with drop bars but also have room for hybrid-size tires and cantilever brakes as well as a somewhat more upright, comfy rider position.