Yep I almost did that first but decided against it because I didn't want to get stuck with no phone in case something went wrong with the process. At that time I was technically on-call for work too.
The store owner told me they serviced a bunch of 4a devices and had lots of experience. They were also suggested by Google as an official repair center with good reviews.
It would have given you time, however, to find a technician with more experience with this model.
On the other hand, the battery problem was physically dangerous, and that should have some bearing.