The author of HM Series fonts has resolved the issue in his new package 'xepersian-hm' located at http://mirror.ctan.org/macros/xetex/latex/xepersian-hm. More information is at http://www.ctan.org/pkg/xepersian-hm.
The README.txt file of the package says:
Kashida feature in xepersian has problem with some fonts such as HM Series
fonts available at 'https://dma8hm1334.bitbucket.io' and XB Series fonts
available at 'http://wiki.irmug.com/index.php/X_Series_2'. The `xepersian-hm'
package fixes this problem.
Consider the following example which uses xepersian-hm:
\documentclass{report}
\usepackage{xcolor}
% \usepackage[Kashida=off,RTLdocument=on]{xepersian} % Load xepersian with a few options
\usepackage[Kashida,kashidastretch=0.14 em plus 0.5 em]{xepersian-hm} % Succeeds
% \usepackage[Kashida,kashidastretch=noskip]{xepersian-hm} % Succeeds
% \usepackage[Kashida,kashidastretch=default]{xepersian-hm} % Succeeds
% \usepackage[Kashida,kashidastretch=kayhan]{xepersian-hm} % Succeeds
% \usepackage[Kashida,kashidastretch=khorramshahr]{xepersian-hm} % Succeeds
% \settextfont[Scale=4.5,Colour=darkgray]{XB XKayhan}
% \setlatintextfont[Scale=2.5,Colour=teal]{XB XKayhan}
\settextfont[Scale=4.5,Colour=darkgray]{HM XKayhan}
\setlatintextfont[Scale=2.5,Colour=teal]{HM XKayhan}
\def\SampleText{راهی جایی تابی چاپی چاههی تلاشهایی شتابهایی تابی چاپی راهی تلاشهــایی که کتابهایی که کلاههایی که}
\setlength\parindent{0pt}
\pagestyle{empty}
\begin{document}
\color{red}
\SampleText \\ \lr{(compiled with: xepersian-hm)~}
\end{document}
The output is:
However, the output of the above example using xepersian is:
