Sand casting produces pieces that need a lot of finishing, compared with precision casting. Precision casting - investment casting - produces a much finer finish. Even then, surface finish depends on how the castings are removed from the investment material. Some processes leave rougher surfaces.
4140 for the steel parts of a musket would not be appropriate. Non-stressed parts can be plain mild steel. 1010/1015 steel. 4140 is not used for parts that require heat treatment like tumblers, springs and frizzens. 6150 is often used for these. Alloy steels must be melted and poured under conditions that will not result in carbon being burned out. If this happens, hardening and tempering become problematic. Mild steels can be surface hardened. Carburized; case hardened. Cheap flintlocks often have case hardened frizzens. Spark for a while before needing work.
Precision cast lock parts require skilled fitting. Sand cast parts would require even more work. And the metallurgy might be unpredictable. Have a good look at Kibler's videos. His flintlocks have precision cast cocks and frizzens. Their complex contours are problematic for machining. The rest of the lock parts are CNC machined. Assembly is easier and predictable, quality control is enhanced. The metal parts fit the CNC precision inletting in the stocks.
Our lock parts were investment cast. Epoxy dies were made using fine original parts as masters. The epoxy dies were used to produce wax patterns, which were set up in ceramic for lost wax casting. Every flaw in the original part is incorporated in the final casting - and there is shrinkage. Machined metal dies produce parts with much greater precision. Dies produced on a CNC machining center should produce excellent castings. Or just forget casting wherever possible, and just CNC machine the parts from solid.
Heating a piece of low carbon steel and quenching it will not harden it. Doing the same with a higher carbon steel will harden it. And leave it brittle. Not good in a barrel. Must be drawn back.
Barrels are stress relieved. Heated under controlled conditions, and allowed to cool slowly. I suspect the Indian barrels are being stress relieved. From everything I have read, the Indian musket barrels are made from tubing.
Want a bit of sticker shock? Price having screws made. If you cannot use screws purchased from stock, and must have them made, the cost will surprise you. A lot of the screws used in antique guns have head profiles and lengths that you will not find in a hardware catalogue. Our top jaw screws cost $1.50 each, almost 50 years ago.
Also consider stock wood. Muskets take long, thick blanks. Walnut is the standard. European walnut would be the standard for Brown Besses. That is going to be problematic from the standpoint of cost and availability. North American black walnut would be the first realistic choice.
I do not think that a 3-D router copy carver is going to cut it, so to speak. You have a very long blank to deal with, and a lot of wood to remove. An industrial grade machine would be needed. Profiling is one thing; precision inletting another.