So I emailed the guys over at Tilt about this battery issue and unfortunately, it seems there is no good answer. Here is what they said:
We don’t have a voltage sensor on the “Tilt 2.0”. As an alternative you can use the “odometer” feature that keeps a running clock of how long the battery has been installed for. The data is in the last byte of the advertising string, normally used for measuring signal strength at 1 meter for iBeacon advertisements. Units are in quarter weeks or weeks depending on the type of caps you have (machined caps or injection molded caps).
The color of the actual circuit board in your Tilt determines the version. A green board is V1 and black is V2.
With all that said, I just don’t know enough about “iBeacon advertisements” to even pull the “odometer” value out of my tilt. But maybe you or somebody else that is smart on bluetooth can figure it out.