Shifting should definitely improve by going from stem shifters to down tube shifters. Simply removing 18" of cable housing will improve things, especially if it was the old spiral wrap housing, which had compression issues.

Check the pivots on the rear derailleur, if ot is a Delrin Simplex. They were suspectible to wear and contributing to sloppy, inconsistent shifting.

I'm not sure as the Atom freewheel was much of a contributor, as least in comparison to other freewheels of the period. However, a modern freewheel with profiled and ramped teeth, and a compatible chain, will make a sunstantial difference. It's inexpensive too, probably cheaper than a NOS Atom freewheel. The only complicator is if you're restricted by French threads but many of the imported French bicycles used English freewheels.