My apologies sir.
Yes a higher gain transmitter would be the first port of call rather than slapping on a PA. I've found some PlayStation 3 microphones that actually use the NRF24Z1, and wrote some micro code to sniff the SPI bus to both the transmitter and receiver to see the config. Was also a good chance to see how a professional product has these things set up. The transmitter - the microphone - uses a single ~23mm monopole on FR4. The receiver uses meander antenna's (two on the board, symmetrical, one going left, the other going right) and the config says both Tx and Rx are at full power - 0dB.
The range isn't great, but it doesn't have to be for that application, it seems to have no cut-outs or glitches providing the two are in the same room, roughly 10m x 7m. It performs significantly better than the test boards I have, with one using a chip antenna, the other a 2.0dbi whip on an SMA. That could be a number of things, most likely the chip antenna, poor matching, and less than ideal PCB layout on the prototype.
As a test, I configured the SMA test board with the channels/address/config for receiving from the PlayStation mic, and range was ok, but not as far as the original PCB printed antenna. It was very sensitive to orientation. Also the receiver PCB is mounted vertically, about 10 degree's leaning back, so the meander antennas are seen ( from the transmitter) from the top-side copper, the Z-axis. So it seems they really did do a rather good job of maximizing range with printed antenna's. But I fear this is the maximum range these devices are capable off given how sensitive they are to bit errors. I'm sure a less time-critical application that allows for multiple resends would achieve far greater range with the given 0dBm output power, 'coding gain' can do quite a bit for range.
As my transmitter is stationary and powered from a wallwart, power is no issue, so I could attempt to design a PCB, with an RF front end (the chip in the first post) and also have the option of a printed antenna, or just an SMA for external. External would of course be easier as I do not have the equipment to tune/match antennas so I would be working blind. But this may not help much, as the receiver must send back data indicated acknowledgements and channel quality. Adding a PA to the receiver, whilst that would extend range, would eat up precious power - trying to keep the power consumption of the headphones to < 60mA. I'm not after '100m' here, but perhaps coverage on one floor, and with multipath fading/reflections, I'm taking a wild guess at +6dB gain required, the 20dB gain seems excessive.
So, I'm thinking... the play station mic design is tried and tested, I'll try to modify that for Rx operation (requires reworking a QFN surrounded by 0402..). The monopole will be quite near the users head, but at least 10mm from anything, I'm sure the housing will detune the antenna somewhat. And for the transmitter, use a board with a PA/LNA, and an external antenna.
Lastly, the external antenna. A whip is fine for omnidirectional comms, but the transmitter will most likely sit, on a desk/surface, close to a wall. It is doubtful a signal will be needed behind it, or to the extreme sides. A more prudent design, to try and maximize range, would be a semi-directional antenna, sort-of hemispherical pattern. One you put up against a wall of a room, and it fills the room, without sending half of the power into the wall (reflections..). I know things can get very hairy with DIY antenna's, but would a patch antenna provide better coverage than say, a 'rubber ducky'? I'm sure the routers antenna is a good 2.0dBi.. but either I don't have a good match to 50ohm, or its just not as omni as the meander antenna.
So, thoughts? I have a habit of over complicating matters (thus the idea of just 'more power!) but it owuld be pretty cool to get some use out of these things, and uncompressed wireless audio is just plain cool.