Switching from high rentrant to linear
Or in more common uklulele terms, "switching from a high 4th string to a low 4th".
You get the best sound when you can match the range of notes in your tuning to the volume of your body. A high reentrant tuning has a range that is more closely spaced than a linear. As such, if you are in, for example, key of C, with a high 4th string, it's a good idea to move to a bigger instrument if you drop that 4th string an octave. You are adding a deeper note, and increasing the range of your tuning.
Conversely, if you switch from a linear tuning to a high reentrant set-up, you move your notes closer together, and lose the low tone of the low 4th string. In that case, you either go to a smaller instrument, or lower the tuning.
In the case of the Baritone, the linear C fits the volume of the body very nicely (better than the standard linear G). If you go to a high rentrant set-up, then it's best to lower the tuning to compensate for the loss of depth on your low 4th.
If I read him right, Stan suggests a high rentrant B to B flat. This is one of those nice alternatives. A bright tuning, but not weak as a high rentrant C would be on the big Baritone body.
With our Medium Gauge strings, you would be a touch lower - key of A, and this may be the best fit of all in terms of body volume to range of notes.
That's not the case with most Baritones - they are made for a heavy wound string set-up, and that's why I would probably go a bit lower, to a high reentrant key of G. This is standard Baritone tuning with a high 4th. It may also be a good fit for a Favilla. My brief encounter with one left me with the impression hat they are somewhat like ours. Not built too heavily, but with a bit deeper body than is generally seen today.
I think the Baritone is due for a re-evaluation. The tonal values of a linear C tuning and a high re-entrant G are pretty close. Both are nice fits for the Baritone body volume, and if luthiers could build to these set-ups instead of the heavy "mini-guitar" linear G strings that have been the standard, this could be a much more responsive instrument in either of these tunings, and much more of a true ukulele.