I received the watch below from a wife a long time ago. It stopped working so 2 years ago, I opened it and I found that the battery was held with a piece of tape like you described. I bought a new movement and replaced it. It did have a few scratch on the "glass" that I removed with Polywatch. This is what it looks like today.
I propose that you just replace the movement in the watch that you have since it will not be a big expense.
PS. You badge says COLA WATCHES. Is there watches with cola logos ?
I buy watches with steel bracelets all the time if the model is offered with that option. It is much cheaper to buy straps after you bought the watch than trying to buy the steel bracelet that fits the watch you bought.
I was at the AD about 1 month ago and someone was asking about this Breitling. I was not paying much attention to the conversation until the man said that this watch had a built-in ELT. The AD said that the watch was discontinued.
Having a PLB (Personal Locator Beacon) as you described it is a cool idea but having something that broadcast on 121.5 as an Emergency Locator Transmitter (ELT) is not a good idea. ELT are installed in aircrafts and automatically starts broadcasting on impact.
121.5Mhz is monitored by the Military, Search and Rescue (SAR) and Air Traffic Control. The reception of an ELT signal at an air traffic control center generates a general alarm to indicate that a commercial aircraft has crashed. The military will contacts the Air Traffic Control to check on the disappearance of an aircraft from radar and also the aircraft type. SAR will get ready to launch planes to locate the beacon. Ambulance service in the general area will also get notified for them to get ready. So it sets the big machine in motion so I could see him being fined and also have to pay for the expenses of SAR.
Occasionally, an ELT can be activated by accident when an aircraft undergoes maintenance at an airport but in that case they know the location is an airport and they will call and ask them what is going on. A ground team will be dispatched to find in the hangar with the ELT broadcast.
https://skybrary.aero/articles/emergency-locator-transmitter-elt
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