Found a solution. What I had was mostly correct, but I needed to flush the ZBuffer, then re-draw my portal triangles to the depth buffer after drawing the contents of the portal.

void RENDER_StartPolyStencil(vertexStruct* v, int n)
{
	glEnable(GL_STENCIL_TEST);
	glDepthMask(GL_TRUE);

	glStencilMask…