Given that you don't like the existing shapes in the available fonts, my other suggestion would be to use tikz to draw the symbol; you can then adjust all parameters and coordinates as you wish.
\documentclass{article}
\usepackage{amssymb,tikz}
\newcommand{\mysetminusD}{\hbox{\tikz{\draw[line width=0.6pt,line cap=round] (3pt,0) -- (0,6pt);}}}
\newcommand{\mysetminusT}{\mysetminusD}
\newcommand{\mysetminusS}{\hbox{\tikz{\draw[line width=0.45pt,line cap=round] (2pt,0) -- (0,4pt);}}}
\newcommand{\mysetminusSS}{\hbox{\tikz{\draw[line width=0.4pt,line cap=round] (1.5pt,0) -- (0,3pt);}}}
\newcommand{\mysetminus}{\mathbin{\mathchoice{\mysetminusD}{\mysetminusT}{\mysetminusS}{\mysetminusSS}}}
\begin{document}
\thispagestyle{empty}
\verb+\setminus,\mysetminus,\smallsetminus+:
\begin{displaymath}
A\setminus B \qquad A \mysetminus B \qquad
A\smallsetminus B
\end{displaymath}
\verb+\mysetminus+ in display, script and scriptscript styles
\begin{displaymath}
A\mysetminus B\quad \scriptstyle A\mysetminus B \quad
\scriptscriptstyle A\mysetminus B
\end{displaymath}
\end{document}
The code provides separate commands for displaystyle, textstyle, scriptstyle and scriptscriptstyle and uses \mathchoice to select the correct one. I have put the textstyle version equal to the displaystyle one. In the \tikz command you can now specify exactly which line to use and what width it should have. I have made the ends of the lines round, instead of square, with the line cap option. Finally, if neccessary you can specify a different bounding box for these characters by addingg the tikz construction
\useasboundingbox (-0.5pt,-0.5pt) rectangle (5pt,8pt);
with appropriate choices of coordinates. (This will avoid the \vcenter type juggling you have in your code.)
Addition If you are worried about the overhead of using a tikz command each time, which I don't think is high in this case, then you can instead of using newcommands use boxes as follows with \newsavebox, \sbox and \usebox:
\newsavebox{\mysetminusD}
\sbox{\mysetminusD}{\hbox{\tikz{\draw[line width=0.6pt,line cap=round]
(3pt,0) -- (0,6pt);}}}
\newsavebox{\mysetminusT}
\sbox{\mysetminusT}{\mysetminusD}
\newsavebox{\mysetminusS}
\sbox{\mysetminusS}{\hbox{\tikz{\draw[line width=0.45pt,line
cap=round] (2pt,0) -- (0,4pt);}}}
\newsavebox{\mysetminusSS}
\sbox{\mysetminusSS}{\hbox{\tikz{\draw[line width=0.4pt,line cap=round] (1.5pt,0) -- (0,3pt);}}}
\newcommand{\mysetminus}{\mathbin{\mathchoice{\usebox{\mysetminusD}}{\usebox{\mysetminusT}}{\usebox{\mysetminusS}}{\usebox{\mysetminusSS}}}}