Looking at the data

the complete schematic is here:

Schematic for RFID1 simulation

Input and output for RFID1. It may be desirable to increase the DC offset or the amplitude of the output
But i'm going to go with this signal to start and work on refining the output after I breadboard the design.

So there are a few ways to increase the strength of the output signal while still maintaining the necessary modulation of the RFID card. I added a small load on the output. This did reduce the over all time the signal was 'high' but it would likely not matter much to the micro-controller.  I increased and decreased the overall inductance and changed the ratios of a few resistors but mostly it led to an instability in the overall output of the signal.  Coilcraft has a few nice 125 kHz RFID inductors on their site that I'm going to add to the BOM and the board layout.

My next step is to work on doing the PCB layout, routing, stack-up, geometry ect and get the board made. Then I'm going to build up and test a breadboard while I wait for the real parts to get in. I'm not going to buy a micro controller yet...I have an arduino device in mind but I'll post another section on this hardware.