I would also like to thank all the professional gentlemen who presented the science and their practical experience with lock springs.
It may boil down to ease of manufacturing for the OP. It is difficult to accurately heat and forge even a small part with an O/A torch without burning carbon out of the sharp edges and underheating the core unless you are very careful, slow, and plan on using a lot of gas, so if he has a good propane forge, anvil, and basic drawing/bending/shaping skills I would think forging is easiest. You don't have to draw the whole taper out both directions with a hammer, that part can be filed and not disturb the "grain" of the metal any if that worries you, not that it should. When thinking of "grain" and "directional strength" of a forging that is to be heat treated, a forged part (such as a drop-forged piece or hammer-drawn spring) is superior to a cast part, but not necessarily superior to a part machined from a bar after the parts are heat treated. I used to argue this point about drop forged parts versus machined parts, both are superior to cast parts but not one better than the other where it simply comes down to the cheapest, fastest, and best production methods. Hand-wrought iron is a different story on account of the slag layers.
The challenge with machining a vee spring lies with fixturing and tracing a curve. To deal with this on a manual mill, I mill or simply saw a straight vee into something like a 1" wide piece of annealed 1095, meeting at a small drilled hole, reduce thickness only as required along the spring edge profile while leaving material for the fulcrum peg, mill the features of both ends of the legs, then turn the piece edgewise in the mill vise and mill down the "outside" of the legs to the desired thickness and taper, then complete the features of the ends. After that the outside of the bend is milled off, peg filed round, width taper is tuned with a file, spring is polished all over, heated and curved as required, reheated and quenched as required, polished again, then drawn in a lead bath.
It's easier, faster, and cheaper to file and beat one out of a piece of rolled spring stock. But if you're cheap like me and have lots of automotive leaf springs stacked up out back, milling works too.
If you want a good model for a machined spring, take the mainspring out of one of Jim Kibler's round-faced locks and trace it. The relaxed shape is dead on perfect for its working range and temper.