This article contains a smoking gun quote which demonstrates the circular nature of using stellar parallax to prove heliocentricity.

“If an astronomer measures the position of a nearby star, and then measures it again six months later”
The assumption that the earth is moving is made before the measurements are taken, it is not a conclusion which may be deduced.
Proofs
- Aristarchus
- Phases of Venus
- Stellar Parallax
- Bessel and 61 Cygni
- Aberration of starlight