I don't have experience with the really old Conns, but I have a strong suspicion that the basic baritone acoustic design didn't really change through the life of the product.
You don't HAVE to have the dill-pickle mouthpiece, although using one of those will allow you to push in and shorten the sounding length so the scale is accurate. Mouthpieces with the chamber the same size or slightly larger than the cork bore will do, too. I use a Meyer on my 1946 Conn baritone (which, I admit, is not a 1917; but I bet it's the same tube).
The problem with these old baritones (and it's not just Conns, and it's not just baritones) is that the scale (the positioning of all the toneholes) was designed based around a mouthpiece chamber volume considerably larger than what's common today. (The old dill-pickle style.) So the scale is VERY ACCURATE if you have a large chamber piece, pushed well in on the neck. When you put a small chamber piece on it, it plays sharper, so you have to pull out - way out. Of course if the small chamber piece has a short shank, the joint to the neck becomes mechanically hinky. If it has a long shank, it'll stay in place; but the problem is that the sounding length has been increased, and the tone holes are in the same place; and all that increase in the sounding length is at the top of the tube. So of course the percentage increase in tube length for high Eb is going to be a lot more than for low Bb.
So when you take that small chamber piece and pull it out, even if it's got a long shank, you have to find some kind of "average" tuning, which most people do by tuing to a note somewhere in the middle of the range. If you get (for example), middle G in tune, the tube's too long for the high notes, making them flat, and it's too short for the low notes, making them sharp. Oldest story in the book. You see the old horns with crescents in the bell tone holes to try to bring them down, and palm keys raised way way up, which just makes the pitch wild as heck. This also leads to some "interesting" tuning anomalies such as the well-documented wicked sharp middle E and F of Conn baritones. It'll make altissimo very difficult and weirdly out of tune, too.
Adding length to the mouthpiece shank will make the mechanical joint more reliable but it doesn't shorten the sounding length or fix the basic issue.
The good news is, you don't have to buy a 120 year old dill pickle that feels and sounds like blowing into an old gym sock. You need, as I noted, something without a constriction in the chamber - something like a Link or Meyer type design. Jody Jazz makes a couple models that might work - I know their bass mouthpiece plays very well on my Conn baritone. Yeah, that Berg 0 or 1 chamber - that's probably not going to work for you. When I went from a Vandoren with small round chamber to a Meyer, I immediately had to push in something like 5/8", and notes that had "tuning anomalies" snapped right into tune. Altissimo started popping out, perfectly well in tune. That nasty habit of squeaking in the palm keys when pushing hard went away. The middle E and F went from wicked sharp to right in tune.
Over the ensuing years, I've found I'm pushing further and further on - till I've got the Meyer for a sounding length that's at least an inch shorter than with the old Vandoren. Just imagine how much of a difference that makes - move any mouthpiece an INCH on the neck and see what it does. I believe that having a mouthpiece properly matched to the scale of the horn has allowed me to use more relaxed embouchure and voicing, which has lowered my basic "input pitch" and improved many aspects of my playing. If you're not fighting the tuning of the thing constantly, you can focus on air and support and that soft yet firm embouchure that's needed.
One last note: don't be fooled by the various mouthpiece shank lengths. The shank length past the beginning of the cork has no acoustical meaning, it's purely for the mechanical joint. If you take measurements, take them to the tip of the MP, not the cork end of the shank.
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