Sorry I wasn't clear in my last post. The link I posted is not to my repository (which is not available online) but just to a repository containing the exact same file so that you could see what it contains.
I made certain that mmc-am3517.c is compiled (mmc-am3517.o is generated and the debug printf's that I added are shown in the console during startup as well).
I think I'm missing some configuration of some interrupt/pin since I get
mmci-omap-hs mmci-omap-hs.0: IRQ Status is 38000 mmci-omap-hs mmci-omap-hs.0: MMC IRQ 0x38000 : ERRI CTO CCRC
where the first line should look like (from the output of the eval board where the MMC/SD slot works fine)
mmci-omap-hs mmci-omap-hs.0: IRQ Status is 1
Furthermore I just realized that the eval board has an SD card slot (where I put in a microSD card in a microSD -> SD card adapter) whereas my custom hardware has a microSD card slot.