I have tried 2 different active HDMI to DisplayPort adapters now and neither have given me resolutions to the LED Cinema Display higher than 1280x720.
Both claim to support 4K at 30 Hz and 1440p at 60 Hz. Neither worked and I'm really bummed. Glad to stumble upon this post, maybe it can help. At this point I'm considering buying a big HDMI converter box. Maybe my DisplayPort to Mini DisplayPort adapter is bad but I feel like that's unlikely.
I use this one for my Switch: https://www.amazon.com/Cable-Matters-DisplayPort-Adapter-Resolution/dp/B00JQORLCG/
And I also have a splitter, both options work just fine.
https://www.amazon.com/Cable-Matters-DisplayPort-Adapter-Resolution/dp/B00JQORLCG/
Can you tell me more about your splitter? What kind do you have?