How to explain why I am applying to a different PhD program without sounding rude?
Concision is your friend here. You do not need to explain all your reasons in detail, and giving multiple reasons will indeed sound negative. Instead, choose the most significant, straightforward reason, and explain it as concisely as possible. In your case, this would be &quot;funding&quot; (#1 and #3 in your list). The issue with coursework, while annoying, does not seem like sufficient reason to transfer (especially when you have presumably already finished many of the duplicate classes).
The challenge with &quot;I want to transfer for better funding&quot; is that grad students are never paid much, and it's a little difficult to believe that the small pay difference between programs is enough to justify starting over, moving, etc., especially when you are otherwise happy with your current program. So, you should provide enough detail to overcome this objection. Note, there is no need to explain the intricacies of your school's internal accounting, just the bottom line (annual salary vs. hours worked). For example:

I am currently paid $15K per year, which barely covers rent in [your expensive city]. So, I have had to work in a grocery story 15 hrs/week just to make ends meet. Further,  my colleagues and I are averaging 35 hrs/week in teaching responsibilities. This arrangement leaves little time for research.