On the oxyacids of +III pnictogens and +IV chalcogens
Disclaimer: This isn't really the answer Jan is looking for. 



Holleman, Wiberg "Lehrbuch der Anorganischen Chemie", de Gruyter, Vol. 101, notes that:

Selenium 

Selenium forms a weaker, but more stable acid based on oxidation state $ +4$. No explicit mention of the structure, which suggests to me that $\ce{SeO(OH)2}$ is the structure.

Tellurium

Tellurous acid's structure is described as unknown.

Arsenic

For arsenous acid (the $+3$ oxidation state based acid) the tautomeric equilibrium is entirely on the side of $\ce{As(OH)3}$ (as opposed to $\ce{HAsO(OH)2}$). The reason given is that $\ce{As}$ does not form double bonds with $\ce{O}$, which is outdated: Current thinking is that only the first row forms double bonds, i.e. no double bonds in $\ce{H2SO4}$ or $\ce{HPO(OH)2}$. Organic esters exist that can be described as $\ce{RAsO(OH)2}$.

Antimony

The $+3$ oxidation state based acid is described as forming $\ce{H+ + [Sb(OH)4]-}$ in water. No mention of tautomerism.

The book gives sources only sparingly and on a per-section basis. Relevant items appear to be:


R. Paetzold: "Neuere Untersuchungen an Selen-Sauerstoff-Verbindungen", Fortschr. Chem. Forsch. 5 (1966) 590-630.
W.A. Dutton, W.Ch. Cooper: "The Oxides and Oxyacids of Tellurium", Chem. Rev. 66 (1966) 657-675.
M.A. Ansari, J.M. McConnachie: "Tellurometalates", Acc. Chem. Res. 26 (1993) 574-578.
J.D. Smith: "Arsenic, Antimony and Bismuth", Comprehensive Inorg. Chem. 2 (1973) 547-683.
C.A. McAuliffe: "Arsenic, Antimony and Bismuth", Comprehensive Coord. Chem. 3 (1987) 237-298. 
GMELIN: "Arsenic", Syst.-Nr. 17, up to now 1 book, ULLMANN, Vol. 5: "Arsenic and Arsenic Compounds", A3 (1985) 113-141.
GMELIN: "Antimony", Syst.-Nr. 18, up to now 6 books, ULLMANN, Vol. 5: "Antimony and Antimony Compounds", A3 (1985) 55-76.




My thoughts on $\ce{As, Sb}$ are that in the MO picture, $\ce{H}$ has insufficient overlap to form a bond that would compete with the alternatives. 



I have performed DFT calculations (PW6B95-D3/def2-QZVP//PBE-D3/def2-TZVP) on gas-phase $\ce{Pn(OH)3}$ and $\ce{HPnO(OH)2}$. Of course, these are gas-phase  energies on single conformers, not free enthalpies. For $\ce{Pn} = \ce{N}$, a 10 kcal/mol favorable energy difference towards $\ce{HPO(OH)2}$ was found. For $\ce{As}$, about 35 kcal/mol towards $\ce{As(OH)3}$ was found. The Mayer bond order analysis was not conclusive.