Can a Polar S610 chest strap with a dead battery be revived?

The battery in my Polar S610 chest strap has reached empty after 4 years of intermittent use. The dying battery manifests this symptom - every time when the watch was moved more than 2cm away from the chest unit, the heart rate display would disappear.

 The slightly wider chest strap centre contained the wireless transmitter. It is flanked by wavy patterned areas on both left and right sides – these are electrodes which make electrical contact with the skin.

The back of the Polar chest strap showing the transmitter and the partially obscured electrode areas. The second row of letter from top says, “Made in Hungary” (blue oval).

The cover to the transmitter is tightly sealed enough to resist the most dexterous prying with a screwdriver. Obviously, Polar did not intend for the user to replace to the battery. ;-) Aha, a chest strap that is meant to be disposed after the battery is flat - how eco-friendly!

A paragraph from the S610 product manual where good corporate citizen Polar promised to recycle the transmitter!

Not to be deterred by a sealed cover, I used a sharp knife (box-cutter) to cut along the cover edges. Opening the rear cover reveals the transmitter Printed Circuit Board (PCB). 

 The label proudly says, “Made in Malaysia” to pander to our nationalistic pride. ;-) So, is the chest strap Hungarian or Malaysian?

The transmitter’s PCB from behind the chest strap. 

After lifting up one side of the PCB, the battery compartment can be seen. It contained a depleted 3V coin battery - Panasonic CR2354.

I can’t find a replacement for the battery despite making many visits to watch shops and electronic components suppliers. It appeared in the 2009 RS (a mail-order component vendor) catalogue. But inquiring with RS, I was told that it has been obsolete. What can I do with a dead chest strap?