Yay, that worked! :)
You were right. pbi_info showed two versions of the open-vm-tools package, the 64-bit I installed via the GUI, and the 32-bit one I have no idea where it came from.
I deleted the 32-bit one via pbi_delete and reinstalled the 64-bit from the GUI; all is well. Service is running, kernel modules are loaded, vSphere Client shows tools as running in the VM.
Thanks a bunch!