Usually death is due to the internal battery. PITA to replace, might as well replace the whole puck.
I used the Pharos-360 (from M$ S&T as well) at first and mine did the same thing and eventually died. I figure less than $50 for a new one is better than my time to open the thing up and replace the battery.
The BU-353 is the size of an Oreo cookie at maximum and then does some weird funky slopes on it so it isnt cylindrical. It is bigger but not by much if I remember correctly. It is magnetic based though so it is really easy to stick somewhere. I am sure you can find room. There is always some trim piece with a cavity if you look hard enough.