I recall reading a calculation which suggested that the LNA+PA version of the nrF24L01+ would not have a huge increase in range for a two-way connection with a regular transceiver; mainly because the receive side would not be much enhanced after SNR was taken into account (apparently the LNA was not that low noise, as the limiting factor for receiving). For one-way transmission from the PA unit or two way between two LNA+PA units, the improvement was much better . Was that post here?
Anyway, a higher gain antenna should help, as it increases signal strength and SNR in both directions. But is it true that higher gain is (almost??) always at the expense of a narrower emission pattern (kinda like using mirrors and lenses with a flashlight - the same power can be emitted weakly in all directions, or more strongly the smaller the focused beam)? And likewise for receive. For the example antenna in this thread, I believe the gain pattern is sort of toroidal - best at right angles to the antenna, less than unity along the axis. To get 9 db this would need to be a fairly flattened toroid (a stepped-on bagel). So in general, antenna gain is not an unambiguous "win", but rather involves a tradeoff which may or may not be worthwhile for a given system.
That can work well for a ranch style house which is mostly 2 dimensional, but for a multi story house the low transmit/receive gain along the antenna axis sometimes needs to be taken into account.