Yes, stick-on gauges are worse than guessing, they can be off by as much as 30F in some tests.
The snake looks to me like it has neurological symptoms, but I am not a vet. There are a variety of possible causes, ranging from an illness (much less likely if the snake is feeding normally), to toxin exposure, overheating or cold shock syndrome, a congenital defect, etc.
Has the snake always had this issue, since you first acquired it?
The vet's suggestion is interesting, do any of your birds have psittacosis, or did he just suggest it because you have birds?