FM demodulator LTspice
So frequency varies from 2,336 MHz to 2,411 MHz

Looking at your demodulating slope detector, it has a Q of about 1.52 and, if I plug numbers into an on-line calculator, I estimate that at 2.331 MHz (slightly lower than 2.336 MHz), the amplitude drop is 0.047 dB compared to that when the frequency is 2.413 MHz.
In real numbers, you should expect to see an amplitude change of about 0.54%. Maybe that's what you see. Nevertheless, it's a pretty poor slope detector if that's all it brings to the party. I would use a high pass filter like this: -


It has a Q of about 10.
At 2.413 MHz the gain is 20.18 dB
At 2.331 MHz the gain is 18.09 dB
The difference is 2.09 dB or, in real terms an amplitude change of 27.2%

Of course you could make the Q a bit bigger and get more conversion of frequency to amplitude. The operating frequency isn't that high to worry about matching loads so you have scope here.