Op's question is what is the correct $\mathrm{p}K_\mathrm{a}\ce{H}$ value of pyrrole. Thus, I'm not going to elaborate OP's findings, but would try to give a reasonable answer to the question. The most reasonable answer I found for $\mathrm{p}K_\mathrm{a}\ce{H}$ value for the pyrrole is $0.4$ (for the novices, this is the $\mathrm{p}K_\mathrm{a}$ of the conjugate acid of pyrrole).
It is well known that the best way to quantify the basicity of an amine is to examine the $\mathrm{p}K_\mathrm{a}$ of its conjugate acid (Master Organic Chemistry). The concept is the higher the $\mathrm{p}K_\mathrm{a}$ of the conjugate acid, the stronger the base.
Let's compare two cyclic amine bases under this concept: Pyridine and Pyrrole. The following diagram illustrate the concept:
Accordingly, pyrrolium ion is about $10^5$ times stronger acid than pyridinium ion. Thus, pyrrole is about $10^5$ times weaker base than pyridine. Why? Read the note on the bottom of the box in the diagram. This is also well explained in chemistry.msu.edu with the diagram attached:
In each case the heteroatom has at least one pair of non-bonding electrons that may combine with the four π-electrons of the double bonds to produce an annulene having an aromatic sextet of electrons. This is illustrated by the resonance description at the top of the following diagram. The heteroatom Y becomes $\mathrm{sp^2}$-hybridized and acquires a positive charge as its electron pair is delocalized around the ring. An easily observed consequence of this delocalization is a change in dipole moment compared with the analogous saturated heterocycles, which all have strong dipoles with the heteroatom at the negative end. As expected, the aromatic heterocycles have much smaller dipole moments, or in the case of pyrrole a large dipole in the opposite direction. An important characteristic of aromaticity is enhanced thermodynamic stability, and this is usually demonstrated by relative heats of hydrogenation or heats of combustion measurements. By this standard, the three aromatic heterocycles under examination are stabilized, but to a lesser degree than benzene. Additional evidence for the aromatic character of pyrrole is found in its exceptionally weak basicity ($\mathrm{p}K_\mathrm{a}$ ca. $0$) and strong acidity ($\mathrm{p}K_\mathrm{a} = 15$) for a $2^\circ$-amine. The corresponding values for the saturated amine pyrrolidine are: basicity $11.2$ and acidity $32$.
Furthermore, for everybody's convenience, I attached a orbital representation of pyrrole and furan to show their resistance to protonation.
Comment on different $\mathrm{p}K_\mathrm{a}$ for pyrrole in literature: The $\mathrm{p}K_\mathrm{a}$ value of $3.8$ (and $\approx 4$) is probably for the protonation of pyrrole at $\ce{C2}$ position. For protonation at $\ce{N}$, $\mathrm{p}K_\mathrm{a}$ is most probably $0.4$, as described above. We can trust the value given in McMurray's Organic Chemistry textbook, since it is widely used in sophomore organic chemistry university course in USA.
