If the mouthpieces have no issues, how do you explain the intonation difference with exactly the same input (air and support) on both? They should be equally flat if chamber doesn't Mayer. It's clear to me the Berg may never play in tune no matter how good the support is. Better to focus efforts on the Link IMO.
My bari player in my quartet plays a hard rubber Link on a similar vintage Buescher, and his intonation is perfect. He is a strong player who uses a lot of air.
I'm sorry, I didn't write my response well.
Here's my opinion:
A berg is probably too small a chamber for a 1930s baritone that was probably designed in 1915 or so. In my opinion, a Link is probably a good chamber size match for this kind of horn (just for reference, I play a Meyer (similar design, but actually a bit smaller effective chamber) on a Conn (also designed, I believe around 1915) and get excellent intonation). While a Link isn't what we might call a "LARGE chamber" (chamber diameter is roughly the same as the cork bore), it's certainly a large chamber by comparison with a Berg.
I would expect that if OP were to get middle G (second line) in tune with both mouthpieces and then measure from the tip of the MP to a convenient registration point, he would find that the Link has a shorter effective sounding distance. This will already improve intonation. But beyond that, once you put a decent size chamber mouthpiece on that old horn, and you start doing some serious airstream work, you're going to find that you want to play progressively looser, progressively more open voicing, and that'll make you play progressively flatter, and you'll push further in, and intonation will continue to improve.
OK, I'm feeling a bit longwinded, so here's my tale.
I've got an old Conn baritone. When I bought it, in the box came a Vandoren mouthpiece with a "small round" chamber. It sounded great, but I had to pull it way way out all the time, and it was still trying to play sharp. I extended the shank 3/4" or so to get it to mechanically work on the horn. But, high notes were flat (so, palm keys raised to the moon), bell notes sharp (especially low Bb), and there were weird tuning anomalies as well (middle E and F darn near a quarter tone sharp, for example).
At some point, after playing this setup for about 20 years, I went on a mouthpiece hunt, found that the Meyer mouthpiece sounds like I want it to sound, and tuned much better. When I adopted the Meyer, the sounding length (measured from the tip of the MP; the amount of cork showing just reflects how long the cork and mouthpiece shank are, no acoustical meaning whatsoever) was about an inch shorter than the Vandoren, to achieve a reasonable in tune position. Now, just to start, reflect on that. An INCH difference in total length! When we tune up we might move the mouthpiece 3/16" or so. It's clear that putting that largER chamber MP (not a "large chamber" that's bigger than the cork bore, just a chamber that's the same size, without constrictions in the window area!) made a HUGE difference to the scale of the instrument, especially up high where any change in length has a bigger percentage effect on the length of the tube.
So when I did this - overall intonation got WAY better - high notes came up, low notes went down - but also the weird tuning anomalies disappeared, altissimo became easily accessible; and a tendency to squeak in palm key notes when pushing hard, totally disappeared.
Now the interesting thing is that over the 20 years since I made this change, my embouchure and voicing, responding to a properly matched sax/MP combination, have continued to get flatter, and I push on a bit further every year. I'd say (without actually measuring) that the sounding length I'm playing this horn with now is at LEAST 1.5" shorter than it was back in 2005 when I had been playing that Vandoren for 20 years.
So, OP, I prescribe a course of long tones and interval studies with that there Otto Link, which I predict will make your bari playing easier, more rewarding, better in tune, and develop a core of rich chocolatey goodness in your tone instead of that buzzy raspy sound that might seem like it projects well but doesn't, not really.