When a heavy quark hadronizes it has some probability of forming a meson vs forming a baryon. I suspect there is a well known branching ratio for each type of hadron. Does anyone know what the probability is or, even better, a reference that discusses this? An ideal answer (though not necessary) would further give a crude approximation of this probability (though I don't know if this is even possible).
Well, you could do worse than skim the classic Lund model:B. Andersson, G. Gustafson, G. Ingelman and T. Sjöstrand, PhysRep 97 (1983) 31 prototype for these things... it is dated, but, hey! you are asking for color flux string basics, not quarz-sharp theory, there.
The diquark to quark pair production ratio for light quarks is, according to their section 3.4, eqn (3.38) about 0.7, so not too far from the Chliapnikov ratio of 0.10 you quote in your supplemental comment. I am only a theorist, but the seasoned combatant experimentalists at the LHC go by the "10 mesons to 1 baryon" rule in their daily routines. (Even more so, the rule of thumb in bottom production is that your b quark is 10 times more likely to end up in a meson than in a baryon.)
But there is an enormous phenomenological cottage industry for this type of prediction, with far too many mechanisms and considerations (spin, flavor, ...) to account for it conceptually.
An easy-to-understand reference with the asymptotic 1/10 ratio in the first figure is Andronic, Braun-Munzinger, Redlich, & Stachel (2011). "The thermal model on the verge of the ultimate test: particle production in Pb–Pb collisions at the LHC", Jou Phys G: Nuclear and Particle Physics, 38 (12) 124081. As a lark, you might consider combinatoric schemes from quark-gluon plasma stretches of the waterfront: E Cuautle and A Ayala, JouPhys: Conf Ser 509 (2014) 012092.