Not entirely sure what to make of this …
I took your FITS image and fed it through IRAF’s DAOPHOT pipeline because I knew that it could compute PSFs and subtract them from images. The image below shows an 8x enlarged view of the region of the transient after computed stars had been removed. With the exception of saturated stars and a scattering of doubles, all the bright stars were invisible, meaning that they had been successfully modeled and removed from the image. A good number of faint stars (one is very obvious in the snapshot) had not been removed because they were too faint for accurate photometry with the parameters I chose.
The double next to the transient is very clearly marked as such: the PSF of a single star has been removed from the mid-point. The transient has been removed nicely but two wings remain. I’d say that was fairly conclusive reason for your astrometric result but for the fact that the other two bright stars also show wings.
As I said, I’m not sure what to make of this but post it for your interpretation which may well be better than mine.
BTW, the image below is inverted N/S with respect to your because IRAF counts pixels from the bottom up. Causes no end of confusion …
Paul