Looking at pages 158-59 in "Confederate Handguns" by Albaugh, Benet & Simmons:
.44 cal. Dance with octagonal-to-round barrel, serial # 20 looks like it has all flat screwheads.
.36 cal. Dance with oct.-to-round barrel, serial # 135 looks like it has a mix of flat and domed screwheads...
The weight of the .44 is listed at 3 lbs 6 oz., so it is lighter than a Colt Dragoon.
Here the .36 cal. guns are listed as generally having 7 3/8" long barrels, although one with a 6" barrel is known.
Looking at pages 278-80 in "Confederate Longarms and Pistols" by Hill & Anthony:
44. cal. Dance with full octagon barrel, serial # 121 clearly has all flat screwheads on the side. It might have a domed screwhead on the single screw at the bottom of the gripframe.
.36 cal. Dance with oct.-to-round barrel, serial # 83; this black-and-white photo shows the underside of the triggerguard and the grip frame screw. It is a little blurred, so determining the shape is difficult, but it looks to me like the two rear screws of the triggerguard might have domed heads...
The barrel on # 83 is listed as being 6 1/8" long. Cylinder length: 1 21/32".
The .44 caliber guns are both listed with 8" barrels and 1 7/8" long cylinders.