Normal Greek sigma (and not varsigma) before apostrophe

Question

Strangely enough, LaTeX automatically changes a normal sigma (σ) into a "varsigma" (ς) if no proper letter follows. Of course, in most cases that's perfectly fine. It's a bit annoying, though, when there's an apostrophe after the sigma because the sigma isn't supposed to change in this particular case.

For example: LaTeX changes my "ἀπολλυσ᾽ οὐχ" into "ἀπολλυς᾽ οὐχ" which I don't like. Has anybody an idea how to fix this?

Here's a minimal example:

\documentclass{minimal}
\usepackage[greek]{babel}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}

\begin{document}
\textgreek{φίλος μ᾽ἀπόλλυc᾽οὐχ ἑκοῦσαν οὐχ᾽ ἑκών.}
\end{document}

Answer 1

Just copying and pasting the code (after substituting c with σ) gives me what I think is the desired result:

% -*- coding: utf-8 -*-
\documentclass{article}
\usepackage[LGRx,T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[polutonikogreek]{babel}

\begin{document}
\textgreek{φίλος μ᾽ἀπόλλυσ᾽οὐχ ἑκοῦσαν οὐχ᾽ ἑκών.}

\end{document}

I get the following if I change the output encoding to utf8x and remove LGRx:

I'm not sure whether using ΄ (U+1FBD) for the apostrophe is correct, but probably you know better.

You get the same result with LGRx and utf8 if you add the following:

\DeclareUnicodeCharacter{1FBD}{\TextGreek{\Psili{}}}