Here's the exact panel I bought, I went with a 7" 1200p display and it uses a 4-lane MIPI DSI controller. eDP panels are typically at least 10 inches, more for laptop than mobile use. So like you I've had trouble searching for eDP to MIPI controllers.Are you sure those HDMI monitors don't use eDP internally? For the panel itself (not the "display", which includes the controller board), it's either eDP or LVDS, and my impression is that LVDS is so old that it's essentially not used any longer. The HDMI tends to be handled by a controller board that converts that HDMI signal to eDP, while (at least on paper) you should be able to connect any eDP source to any eDP target with just a simple cable, no controller board needed (though you'll lose any OSD functionality through this, of course - just like a laptop).
Edit: ah, I forgot, if the panels are made for mobile use they might also be MIPI DSI. If the monitor you ordered is the 8.9" one you mentioned above, that sadly looks like it's DSI and not eDP And all I can find when searching for eDP/DP to MIPI DIS is controller ICs, no actual converter boards. That sucks.
(Oh, and that board you linked is USB-C, no? So it's likely DP alt mode-to-eDP?)
The smaller board closer to the panel has the 40-pin MIPI connector but it's not as straightfoward as using a cable that with eDP at the other end. As you said, it requires a board with the controller to actually convert the signal that supports this model display.