The good news is that :
- Roman found LucidChart.com,
- he was able to import that complex Visio diagram into it, and
- the end-result looked good enough (after a couple import fixes).
So I went to LucidChart.com to try it out :)
I have done a LOT of Visio diagrams (in the past), and I have to say that I found Lucid Chart's web interface really easy to use (and learn).
As a test, I imported an image from this blog, and was able to quickly create this:
Not bad for a couple minutes work :)