How to repair broken (partially snapped) proximity (RFID) card?

I have been issued a proximity card that allows me into my parking lot. I recently partially snapped it in two (easier than you might think). As expected, it no longer works. I was reading and it seems possible to fix it.

Some ideas I was thinking about to fix it (ordered from easiest to hardest):

1. Find a similar prox. card and swap the broken coil out for the working one (don't have another card on me though)
2. Wind my own coil and replace the broken coil with that
3. Solder the breaks in my broken coil

Here is a picture of my broken card:

In the last image, you can see there is no way to separate the two halves with a knife.

To open the card and gain access to the wire coil I have a few ideas:

• Using acetone to dissolve the plastic. I'm not sure if this would damage the copper coil or integrated circuit though.
• Using a blow dryer to heat the plastic. Not a good idea, because the heat could damage the IC before the card even begins to separate. Maybe, if I were very careful, I could heat only in the crack, and thus avoid any damage to the PCB

Can you help me fix my card?

EDIT:

Card sitting in "Really Powerful Nail Polish Remover"

There were three layers. The bubbly, pealing one is the second, the clear plastic on the side is the first, and the smooth layer is the third.

EDIT #2:

Card is dissolving more. It looks like the coil is circular.

EDIT # 3:

The coil is indeed circular!

And I think I found the root of the problem:

The PCB has become disconnected from the coil. I'm unsure if this happened because of the extraction of the coil, or if this was the cause the card stopped working.

Either way, I'll now attempt to solder the coil back to the circuit board then check the continuity. After that, a test is in order. Hope this goes well!

EDIT #4:

No. Coil didn't seem to have continuity and when connected with the PCB, it didn't function.

Next thing to try is to make my own coil