Sorry, that’s what I meant by selfmade IR gateway, when hooking up a single IR transmitting LED to and ESP8266 
Personally I had a pretty bad transmission range with a very similar, if not the same, IR transmitter module - only about 1-2 metres or so.
You really should get it very close to your TV first just to make sure if it might be the LED transmitter range or possibly something still with the signal repetition, or also try with any other IR device and remote which you might have at home.
The best IR receiver and transmitter in the past for OMG was the Avatto/Bakeey IR blaster. Unfortunately the newer models are not with an ESP8266 inside any longer, but a custom chip which is not compatible with OpemMQTTGateway.
You can read about it in this thread
As you also seem to be in Germany (from your Ali link above) you might want to risk a purchase, to see if any of the S06 remotes offered in German online stores are still with the old ESP8266 inside just make sure it does NOT mention Tuya compatibility anywhere! It would also require an FTDI for the first initial OMG upload.
Even this one on eBay Germany seems to have the same package as my old versions, without any Tuya mentioned anywhere