Indeed. Another fact you can use is that in Newtonian mechanics (although not in GR due to frame dragging, only approximately), a rotating spherical body has th

Indeed. Another fact you can use is that in Newtonian mechanics (although not in GR due to frame dragging, only approximately), a rotating spherical body has the same gravitational field as a static one. So there would be no mechanism for the axially tilted rotating Earth to influence the Sun (different from a non-rotating Earth).