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 "funding" (#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 "I want to transfer for better funding" 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.
Actually, I don't see how "inadequate financial support to allow me to continue" would seem rude. You don't have an issue with the professors or what you are learning so I think you are safe enough discussing your decision with them. Maybe knowing your situation would encourage them to free up any available funds.
Probably many of your professors had to struggle themselves with finances in their own education. It isn't uncommon. Maybe they will have some suggestions, both locally and to expedite a change.
But they can't help you if they don't know. Ask.
I'm surprised, actually, that your doctoral program doesn't cover all fees. That is pretty unusual, unless you are at a private institution.
Speaking as a doctoral coordinator, I would encourage you to focus your efforts on seeking a better program fit for your research interests and career aspirations. No one wants to admit a doctoral student that was a "problem" from someone else's program. Focus on the positive. This year will be very competitive for most doctoral programs - what do you bring to the table compared to a new applicant with no prior history?
You should have known all about the fees and financial support before starting in your current program. In my opinion that is not a valid complaint. I would not cite this at all.
If you really are being asked to work each week more than the amount of time specified by your GA contract, that is against university policy and the law. It should be reported to the Department Chair, Dean's Office, and ultimately the Provost at your school (if it is not adequately addressed inside the college). It puts the university at financial and legal risk if individual faculty are abusing graduate students.
If you are simply being asked by your assigned advisor to put in more work than your peers who are assigned to other faculty, but not an amount of time that is specified by the GA contract, that is a different case. Again, that to me is not a valid complaint. You could request a different assignment, but as long as you are not being asked to perform work that exceeds your GA commitment (20 hours, I'm guessing), you really don't have a good case to complain.
I hope that helps. Good luck!