Buffering/matching large signal to drive 5 ohm capacitive load at 13MHz (RF)
As in your description, the FET source follower works to certain extent but with distortion. The source of the distortion is probably not exactly because the signal amplitude is too large, but a secondary effect to that. You mentioned a 12V power supply and 7V signal (assuming the signal is centered), so at the low end, the signal would be at around 2.5V. Most likely, that is too low to turn on the FET adequately.

So maybe give this a try -- bias the base of the source follower FET to around 8V with couple of resistors. Capacitively coupled the input signal to that.

As to matching the impedance, typically, the requirement to match the impedance is because the amplifier is designed to only work at a certain load impedance. That does not seem to apply in what you are doing, so there is no need to match impedance. The amplifier just needs to have enough drive (low enough impedance) to get the signal level that you want.