Where is this extra energy in the Hydrogen Atom coming from? The mass of hydrogen is 938.783073804(56) MeV/c^2
The mass of a proton is 938.272088163(35) MeV/c^2
The mass of an electron is .510998949(97) MeV/c^2
The mass defect is thus   -.000013308(84) MeV/c^2
The ionization energy is   .000013598(43) MeV      (with relativistic and nuclear corrections)

Data from NIST and CODATA. Hydrogen should be equal in mass to a proton plus an electron minus the ionization energy, but acccording to the above, a hydrogen atom is 0.290 electronvolts heavier/more energetic than that would suggest, and this difference is statistically significant.
The ionization energy takes into account the kinetic energy of the electron, and I would assume the kinetic energy of the nucleus in the center of mass frame is zero, so where is this extra energy coming from? For reference, this difference is about 3 times larger than the maximum predicted mass of the electron neutrino, so not an insignificant clerical error!
 A: Your mass defect result 13.3 eV is indeed too low, it should be around 13.6 eV. Most of this discrepancy (0.3
eV) is most probably not real, otherwise basic textbooks would have to rewritten. CODATA gives proton and electron masses and those numbers should be quite reliable. They do not give hydrogen atom mass so it is from some other source which is most probably not guarranteed to be consistent with CODATA.
It is difficult to measure mass of neutral hydrogen atom to similarly high accuracy as the mass of the proton, because the atom is electrically neutral and quite unstable (forms $H_2$ molecules or ions). I do not think digits in 938.783073804 MeV/c2 after 6th decimal are certain to be correct.
To investigate this further I would go after how this number was determined, or how in general hydrogen atom H1 mass is best determined. Direct measurement of mass is probably problematic, resulting in low accuracy result. It may be that the more accurate way is actually the indirect way, assuming atom mass = mass of proton + mass of electron - ionization energy (known from spectroscopy).
