Hi Micha,
I use Kodi and Hyperion as well with TVheadend on x86 base. My tuners come from a FritzBox Cable however.
The behaviour of Kodi and Hyperion is normal for me on both, TV signal and movie files.
I don't have a clue where this flickering could come from.
Have you thought about detaching the LEDs from the Raspberry by using Wemos D1 mini boards in combination with WLED?
This works REALLY great and flawlessly + it would solve your SPI port problem. Also you can place the RPi somewhere else.
And I could imagine, that the dedicated signal processing to the LEDs might be an advantage for your setup
You can have a look at my setup here:
First of all thank you so much !!! Team Hyperion !!! for bringing this nice project to the community and making it so easy to understand, that even guys like me can have a setup

Let me show you, what I have done so far:
youtube.com/watch?v=NiMZ6aSeOZY
It is an LG 55" OLED Display with Yamaha AVR and Nubert 5.0 sound system. Hyperion is installed on x86 hardware with LibreELEC Media Center Software and TVheadend. The LEDs are SK6812 RGB(N)W connected to two Wemos D1 Mini. 108 LEDs on the…
I ran Hyperion cabled via Arduino before, but for now, I will never ever do anything else then WLED.
edit: just noticed, that you are building a T2 receiver - so WLED might not be an option for you ?