So I got a mini display port to HDMI cable + a HDMI to display port
adapter. It does not work. It all seems to fit fine, but the monitor
Because it isn't an "HDMI to DP" adapter, but a "DP++ to HDMI" adapter, which picks (ONLY) the TMDS signal (what HDMI uses) output from a DP++ source to an HDMI sink (e.g. monitor).
So I got a mini display port to HDMI cable
And this is pretty much an DP++ to HDMI "adapter" as well.
So as you could have imagine, your connection is something like this:
(Mac) DP++ --> HDMI|HDMI <-- DP++ (Monitor)
And obviously it's only natural that it won't work.
P.S. IF the mini-DP port of your Mac isn't a DP++ port (though it should be), your mini-DP to HDMI cable won't work either even if you connect the HDMI side directly to an HDMI monitor. In that case you will need an active (i.e. involves signal conversion) mini-DP to HDMI adapter.
To convert HDMI/TMDS signal to DP signal "again", you will need an active HDMI to DP adapter (which seems to be rare).