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It is not likely that a filter designed for 13.56 MHz would have significant loss at 13.8 MHz because standard designs set the cutoff frequency at about 1.2 times the “nominal” frequency. Maybe something else is wrong. You could try decreasing the capacitor values by about 10% but I don’t think this will work.
As for calculated parts values, there are a couple of ways to find parts for filters. One is to use the closest standard values. For this type of low pass filter use the closest smaller standard value for the inductors and capacitors. This will raise the cutoff frequency but there is plenty of tolerance for this before the second harmonic will pass. Generally, these filters are designed to have the cutoff frequency 1.2 times the operating frequency. There will be little harm if this is raised by the smaller value components (within reason).
Another approach is to wind your own inductors. This would involve obtaining some toroid cores suitable for the frequency of operation and calculating the number of turns required.
The loss you observed could be due to the filter if the inductors or capacitors have high loss at 13-14 MHz. Using the correct toroid cores and low loss capacitors I have observed loss of about 1 dB (about 11%) in a 5 pole filter at 1680 kHz.
You might also consider the use of the 2N3053. This has a rather low gain-bandwidth product (Ft) of 100 MHz. One with an Ft of 300 to 500 MHz would probably work better.