This is interesting and thanks for posting those links.
It seems to me that the concept of the
Hegyestőr in Hungary and it´s specifications differs depending on which time period one is looking at. In Polish literature
Koncerz means basically the over-long
Estoc with Hungarian hilt from the 17th century onwards. Going through the information provided by you - and this makes sense since this weapon interpretation came from Hungary most possibly - discussed weapon (here the
hegyestőr) design has in fact been shorter and carried by the belt.
"A hegyestőrök a 15. században jelentek meg, Stiborici Stibor a sírkövén jobb oldalára fölkötött hegyestőrt visel."
(Hegyestőr appeared in the 15th century, Stibor Stiborici wears a Hegyestőr tied to the right side of his tombstone.)
"A katonák nem a derekukra kötötték, hanem a nyereg jobb oldalára
erősítették."
(The soldiers did not tie it around their waists, but attached it to the right side of the saddle.)
Source:
https://hu.wikipedia.org/wiki/Hegyest%C5%91r