:tada: :tada: :tada:
You were right; there was a minuscule piece of wire strand between two contacts and after removing it all is fine now.
Also checked all the radio's again which is easy now I have a working configuration and there was indeed one defective radio module.
Thanks everyone for unblocking me!

@NaCl
No, it did not work as expected. It could not provide enough power for my application. I ended up buying a more powerful setup (10W solar panel + included controller/BMS) with 4 Li-Ion cells and a 3V3 step down converter.

@electrik : downgrading the board definition to 1.0.0 worked. I can now build the ESP32 gateway.
However, I'm not quite there yet, because I get an endless series of "Brownout detector" messages:

Brownout detector was triggered

ets Jun  8 2016 00:22:57

rst:0xc (SW_CPU_RESET),boot:0x13 (SPI_FAST_FLASH_BOOT)
configsip: 0, SPIWP:0xee
clk_drv:0x00,q_drv:0x00,d_drv:0x00,cs0_drv:0x00,hd_drv:0x00,wp_drv:0x00
mode:DIO, clock div:1
load:0x3fff0018,len:4
load:0x3fff001c,len:808
load:0x40078000,len:6084
load:0x40080000,len:6696
entry 0x400802e4
17 MCO:BGN:INIT GW,CP=RNNGF---,REL=255,VER=2.3.1
21 TSF:LRT:OK
23 TSM:INIT
24 TSF:WUR:MS=0
30 TSM:INIT:TSP OK
32 TSM:INIT:GW MODE
34 TSM:READY:ID=0,PAR=0,DIS=0
39 MCO:REG:NOT NEEDED

Brownout detector was triggered

I have the wireless gateway and Mosquitto running and now I can see the temperature readings coming into node-RED, nicely decoded through mysdecode.
Thanks everyone for these amazing frameworks!

Thank you for your setup example. It is nearly identical to my setup (only I use RFM69HW's).
The only thing I can think of now is that the radio modules must be defective, but I have no means to test this) So I ordered a new batch of RFM69's and hope for the best...

[Edit]
I see that you do not use the following defines as instructed in link text:

#define MY_RFM69_IRQ_PIN D1
#define MY_RFM69_IRQ_NUM MY_RFM69_IRQ_PIN
#define MY_RFM69_CS_PIN D8

I have tried both with and without these defines, but it makes no difference.