I believe Eric Johson was a barrelmaker. I've seen guns with his name on the barrel before. Is the firing pin on your Ballard a rectangular shaped pin? You should be able to see the shape under the hammer. Is the extractor the type that slides straight back on a round shaft bored into the receiver on the left side, or is it an extractor that pivots open on the action screw? If it slides on a shaft, it's a Ballard #3 action. If not, it's probably a #2 Hunter, or other action. 
Do the double set triggers serial number to the action? If so, and if it's a #3 receiver, it might well have been a #F, as they often had set triggers.

Got the Ballard out of the closet.  The firing pin looks to be round, not rectangular. Maybe a lot newer than the rest of the action.  Might it have been redone when this was converted to a .22 RF gallery rifle? 

And the extractor is one that slides straight back on the left side of the receiver.  I do not see any numbers on the DST.  They are case hardened and look a lot cleaner and better preserved than the case hardening on the rest of the receiver.  The DSTs fit the action perfectly.  I assume they are original and are in better condition because they are inside the action.

There is a part of the action where a tang sight would fit that is not as worn as the rest of the action.  When the Ballard was in its original condition, it apparently sported a tang sight.  Now there are no iron sights, only scope blocks.

The stock and particularly the fore-end are OK but somehow just look out of place on this old girl.  Aluminum inlays?  What's next?  The whole thing looks like 1950s moderne.

I got the rifle from a couple of hicks who were using it to shoot rats in a barn.  They were shooting .22 shorts or BB caps and screwed up the forward end of the chamber with lead deposits until a standard .22 LR would not chamber.  The abuse of the rifle irritated me badly.  I gave them some $ on the spot and took the rifle home.  My gunsmith got the crap out of the chamber and now the rifle seems to shoot like a target rifle, but I still need to give it a long day or 2 at the range.

The extractor type you described is the style used in all .22 RF Ballards, such as the #3's, so I'd guess that's what it is. The firing pin was probably changed, as all #3 Ballards, and almost all #2 Ballards used the rectangular firing pins. The difference between #2 and #3 firing pins is the #3's weren't reversible, being rimfire only.
The serial numbers can't be seen on the trigger group/block, unless you drop it out of the frame. I'd guess if it has the round firing pin, and the set triggers, maybe they just changed the entire breechblock to get the set triggers.
Sounds like a great old Ballard regardless, and these minor changes are very common in single shots of this era, (Ballards especially).