You should be able to clean the screws up. First find proper screwdrivers. Gunsmith drivers would be great but the hollow ground tapered flathead bits in a driver set work well too. Just make sure they are the correct size. Standard hardware store screw drivers are made to booger up the screws of lawn mowers and Chinese toys.
Remove the screws and secure them in a padded vice or pliers.
With a fine file gently file away the burs and re define the slot.
Next take a cup, a paper cup is fine, fill about 1/3 full of water with a little cooking oil added to the surface of the water.
While holding the repaired screws with pliers heat then with a propane torch 'till they turn blue, then drop 'em in the cup. Done!
Make sure there is no gap at between the frame and barrel assembly where they meet below the cylinder. There should be some gap between the cylinder and barrel cone but not too much. The cylinder to barrel gap is more on a BP revolver than a modern one. Also I believe the Colt gap is wider than the 1858 Remington due to the open top design. A photo would help.
By the way the Colt cylinder actually slides forward slightly to the barrel cone when you cock it. It should click out COLT or Click Click click Click.