Hi, Buckshot!
From your description, sounds like the trigger spring tension is too light. Check that, and while you are at it, see if the filing done on the locking bolt has made it's tension too light as well.
Replacement parts for the 1860 Colt are cheap. Try Dixie Gun works for the spare Italian repro parts.
If you plan to shoot that repro revolver extensively, you might consider spare parts as follows:
trigger, hammer, hand, hand spring, trigger/locking bolt spring, spare locking bolts, nipples, frame screws, mainspring.
As much as we love those old single-action Colts, they used to be called "the gunsmith's friend" because of the frequent (and common) repairs needed.