Specifics on connecting RFM69 to pi3

Question

I am trying to follow these instructions to test a RFM69 module added to an Raspberry Pi 3.
This is likely rather naive, but I would like to know details on how to connect the pi to the module.

The RFM69 module has a 2x20 "female header".
The pinout section in this documentation lists this as required pin connections:

• RST hole on radio (Radio reset) -- GPIO25 (Pin 22) on the Pi
• CS hole on radio (Radio SPI Chip Select) -- CE1 (Pin 26) on the Pi
• CLK hole on radio (Radio SPI Clock) -- SPI SCLK (Pin 23) on the Pi
• DI hole on radio (Radio SPI data in) -- SPI MOSI (Pin 19) on the Pi
• DO hole on radio (Radio SPI data out) -- SPI MISO (Pin 21) on the Pi
• DIO0 hole on radio (Radio digital IO #0) -- GPIO 22 (Pin 15) on the Pi

I had originally assumed that the female 2x20 header in the RFM69 could be directly connected to the male 2x20 header on the Pi.
I now suspect it is not that simple because:

1. when doing that the male pins on the Pi3 could not be pushed all the way into the female receptacles on the RFM69 module, and,
2. the description of the pinout in the documentation makes no mention of the 2x20 header

I tried using jumper wires to connect the holes in the RFM69 to the pins on the Pi3 but they do not fit snuggly, so I am wondering what's the "right way" from doing this.
I am avoiding soldering anything to the radio as I am afraid I might damage it (and the pictures in the documentation suggest the connecting should be easier than that...

Does anyone has detailed instructions on how they connected and successfully an RFM69 module to their Pi 3? Please, be specific as possible: for instance, what kind of wiring was used to connect.

Added 2021/01/13: The problem I seem to be having is that there are 4 pins in the Raspberry Pi 3b+ that were not there in previous versions of Raspis 3s that do not let the bonnet to be connected all the way: see figure. Does anyone know what those pins are?