...
It starts to look like Win32 does not like the sharing of HDC... (despite of what the documentation says).

What about this:

void RenderCharacterSys(FontGlyphConsumer& sw, double x, double y, int ch, Font fnt)
{
	RLOG(CoWork::GetWorkerIndex() << " RenderCharSys " << fnt << " " << ch << " " << (char)ch);
	static Atomic h;
	h++;
	HFONT hfont = GetWin32Font(fnt, 0);
	VERIFY(hfont);
	if(hfont) {
		HDC hdc = CreateIC("DISPLAY", NULL, NULL, NULL);
		HFONT ohfont = (HFONT) ::SelectObject(hdc, hfont);
		GLYPHMETRICS gm;
		MAT2 m_matrix;
		memset(&m_matrix, 0, sizeof(m_matrix));
		m_matrix.eM11.value = 1;
		m_matrix.eM22.value = 1;
		int gsz = GetGlyphOutlineW(hdc, ch, GGO_NATIVE|GGO_UNHINTED, &gm, 0, NULL, &m_matrix);
		if(gsz < 0) {
			LOGFONT lf;
			int ret = GetObject(hfont, sizeof(lf), &lf);
			RLOG("Failed " << CoWork::GetWorkerIndex() << " RenderCharSys " << fnt << " " << ch << " " << (char)ch
			               << ", real: "  << " " << lf.lfFaceName << " " << lf.lfHeight);
			RDUMP((void *)hdc);
			RDUMP((void *)hfont);
			RDUMP(GetLastErrorMessage());
		}
		VERIFY(gsz >= 0);
		if(gsz < 0)
			return;
		StringBuffer gb(gsz);
		gsz = GetGlyphOutlineW(hdc, ch, GGO_NATIVE|GGO_UNHINTED, &gm, gsz, ~gb, &m_matrix);
		if(gsz < 0) {
			LOGFONT lf;
			int ret = GetObject(hfont, sizeof(lf), &lf);
			RLOG("Failed2 " << CoWork::GetWorkerIndex() << " RenderCharSys " << fnt << " " << ch << " " << (char)ch
			               << ", real: "  << " " << lf.lfFaceName << " " << lf.lfHeight);
			RDUMP((void *)hdc);
			RDUMP((void *)hfont);
			RDUMP(GetLastErrorMessage());
		}
		VERIFY(gsz >= 0);
		if(gsz < 0)
			return;
		RenderCharPath(~gb, gsz, sw, x, y + fnt.GetAscent());
		::SelectObject(hdc, ohfont);
		::DeleteDC(hdc);
	}
	h--;
	VERIFY(h == 0);
}