tikz: wonky spacing even with "on grid"

Question

I'm a newbie making a simple flow diagram using relative positioning and on grid. My diagram is simple, so I expected everything to line up easily. But I'm getting this:

I'm trying to draw arrows from the right-most nodes to some invisible placeholder nodes on the right margin (using [coordinate]), and I'm lining those up relative to the center line. But something is wonky.

Am I missing something basic? My code:

\documentclass[letterpaper,11pt,reqno]{amsart}
\usepackage{tikz}
\usetikzlibrary{positioning,shapes.geometric}

\begin{document}
\begin{tikzpicture}[nodes = {draw,font=\ttfamily\footnotesize, inner sep = 1pt}, on grid]

  % nodes on the main line + coordinate placeholders
  \node [circle] (1) {1};
  \node [circle, right=10mm of 1] (2) {2};
  \node [coordinate, right=10mm of 2] (3g) { };
  \node [circle, right=10mm of 3g] (6) {6};
  \node [coordinate, right=10mm of 6] (7g) { };
  \node [coordinate, right=10mm of 7g] (8g) { };
  \node [coordinate, right=10mm of 8g] (9g) { };

  % other nodes
  \node [circle, below=1cm of 3g] (3) {3};
  \node [circle, below=1cm of 7g] (7) {7};
  \node [circle, above=1cm of 8g] (8) {8};
  \node [circle, below=2cm of 9g] (9) {9};

  % right edge coordinate placeholders
  \node [coordinate, right=10mm of 9g] (edge) { };    
  \node [coordinate, above=1cm of edge] (edge_above) { };     
  \node [coordinate, below=1cm of edge] (edge_below1) { };     
  \node [coordinate, below=2cm of edge] (edge_below2) { };     

  % paths
  \path[draw]
        (1) -- (2)
        (2) -- (6)
        (2) |- (3)
        (3) -- (7)
        (7) |- (9)
        (6) |- (8);       

  % right arrows
  \path[draw, ->]    (8) -> (edge_above);
  \path[draw, ->]    (6) -> (edge);
  \path[draw, ->]    (7) -> (edge_below1);
  \path[draw, ->]    (9) -> (edge_below2);
\end{tikzpicture}
\end{document}

Answer 1

I suppose there could be some improvements to your scheme, but to fix your problem, here's the solution: delete the coordinates, and rewrite your last arrows like this:

\draw[->] (8) -- ++ (2.5,0) coordinate (eight);
\draw[->] (6) -- (6-|eight);
\draw[->] (7) -- (7-|eight);
\draw[->] (9) -- (9-|eight);

Basically, the first arrow (top one), goes on for 2.5cm and establishes a coordinate eight at that point. Then, using the TikZ operator -| we can draw arrows from the other nodes that go on, horizontally (-) until they reach the same vertical position of eight (|) and there, they stop.

Here's the result: