I'd think that it can be done with 'standard' baritone string sets.
I've done similar experiments with the following:
Tenor uke, a full minor-third DOWN, tuned to re-entrant E-A-C#-F#, using Martin M620 strings. These strings the 'C' string is 0.0340" which is thicker than any other tenor all-non-wound set I've tried. Tension is fine, and sustain is like forever.
Baritone uke, a whole step DOWN, tuned re-rentrant C-F-A-D, using Worth Clear CF (their FATTEST set). Tension is ALSO fine, and sustain is forever.
The trick to tuning DOWN from standard, with NEW strings, is NOT to tune them up to concert pitch at all, for once they settle at that tension at concert pitch, if you tune them down afterwards, they are like rubber bands and will not only not intonate well, but sound pretty dead.
As far as tuning UP, you can use thinner strings. However, I did try to use the Oasis Warm re-entrant set to get GCEA on a baritone, and after a while, they just stopped tuning up, and then kept going flat the more I tuned them, which told me that all the elasticity was gone and the strings ruined. I threw them away.
Using my 2 previous examples for achieving a LOWER tuning right at the start with a fresh set of new strings, I'm thinking that for Eb re-entrant on a baritone, you could use either the Aquila GCEA baritone strings that come both in standard nylgut and also the LAVA flavor, and when tuning UP to pitch, just dont tune ALL THE WAY up to GCEA, stop at Eb, and see if they have enough tension. Aquila strings are cheap enough to try both styles of string sets. The LAVA strings are significantly thinner in diameter than the nylgut, and feel more like fluorocarbon than nylgut.
Also, if you are not opposed to traditional NYLON strings, you could use the D'Addario string tension calculator web app, which is NOT the old PDF file they provided whereby you had to do that math yourself, with the web app you can input all the variables you want and it calculates for you.
However, when you start it, tell it that you have a 'CUSTOM INSTRUMENT' and then say NO to the 'USE EXISTING STRING SET AS STARTING POINT', tell it '4 STRINGS' and scale length 19 or whatever you instrument is, put in your desired tuning, and then set all 4 strings to NO END, HOMOGENOUS and NYLON, and then at the end where it gives the option for string tension vs. gauge, use the tension option, and put in 12lbs for all 4 strings to start (most uke strings across all manufacturers and scale lengths are somewhere between 10-15 lbs per string or 40-60 lbs per set), and then click on GET RESULTS and it shows you the gauges it comes up with.
After that point you can fiddle with all the settings and use the +/- buttons to adjust the string gauge and it gives the tension. All of the sections of the settings will need to be 'expanded' horizontally to view/adjust them again, and as you change them the part with the string gauge/tension will show the new values automatically.
see the web page here:
http://www.stringtensionpro.com
Once you have your set built, you can then go off to juststrings.com or stringsbymail.com and by them as singles as per the gauges you came up with.
I've been using this web app extensively myself to come up with string sets for fifths tuning for linear CGDA on tenor and linear GDAE on baritone and am quite happy with the results...(I posted recently about that over here:
http://forum.ukuleleunderground.com...7-Tuning-ukes-in-fifths&p=1779628#post1779628)
Hope the above helps, at least a little bit...