Which nRF24L001+PA+LNA should I get?
The range you quote seems extremely low.

Friis' transmission equation tells us that, all things equal (we will come back to that) higher frequencies suffer more signal loss. It states:

$$ \frac{P_{R}}{P_{T}} = G_{T}G_{R}\Bigg(\frac{\lambda}{4\pi R}\Bigg)^2 $$

Where:


\$P_{R}\$  and \$P_{T}\$ are the received and transmitted powers in Watt
\$G_{R}\$ and \$G_{T}\$ are the receiver and transmitter antenna gain
\$\lambda\$ is the wavelength in meters
\$R\$ is the distance between the antennas (actually their phase centers). 


Note that this only applies in the far field! 

The dB version:

$$P_r = P_t + G_t + G_r + 20\log_{10}\Bigg( \frac{\lambda}{4 \pi R}\Bigg)$$

For now, let us ignore the \$G_t\$ and \$G_r\$ terms, since in general they will be pretty close to one. 

The datasheet can give us a lot of information. To get an estimation of the range, what we need to look at is the received signal strength the device needs in order to, in the best case-scenario, operate. 

On page 15 of the nRF24L01 datasheet There is a table "Transmitter Operation". It tells us for the maximum output power (typical):

$$P_{RF} = 0\ \text{dBm}$$

On page 16, we find the "Receiver operation" table. In this table, we can see that:

$$RX_{SENSE2}= -82\ \text{dBm}$$
$$RX_{SENSE1} = -85\ \text{dBm} $$

The received power is the transmitted power minus the power lost along the way. In symbols:

$$P_{R} = P_{T} - PL$$

Where


\$P_{R}\$ is the received power in dBm
\$P_{T}\$ is the transmitted power in dBm
\$PL\$ is the path loss, in dB (Not dBm!)


In other words the maximum pathloss the system tolerates at 1Mbps communication rates is:

$$PL_{MAX} = P_{T}-P_{R} = 0 \text{dBm} + 85 \text{dBm} = 85 \text{dB}$$

That means that

$$PL_{MAX} =  20\log_{10}\Bigg( \frac{\lambda}{4 \pi R}\Bigg) $$
$$R = \Big(10^{\frac{PL}{20}}\cdot \frac{4\pi}{\lambda}\Big) ^{-1} = 140\ m$$

That means that if you use half-decent antennas, no external amplifiers, it should work to about 140 meters. Ofcourse, in practice you will never reach this range. So, pretty much any board that uses the chip and hasn't been poorly designed will easily meet your requirements. (20 bytes within 5ms is about 32Kbit/s, so you have 968Kbit/s to spare).

What could be happening is the following:


A lot of other devices are causing interference
You put the antenna too close to metal (the enclosure?)
The boards you use are just really, really, really poorly designed.


I would suspect a board with extra PA can do more harm than good, since it might actually cause noise and/or oscillations.

The performance of an external antenna could allow you to mount the antenna far enough from any materials you don't want close. 

On re-reading your question, I noticed you saying:
"These 10 meters will not have walls, but musical instruments". Is it possible that you are trying to use these modules very close to human bodies? If so, they could be an issue.