I resolved it. In case someone is curious...
Using the Internet Options control panel and inspecting the Add-Ons, I found out the individual DLLs corresponding to the Reader XI software as well as their CLSID as they were referenced in the registry. I felt I could try to remove registry references and then try to install Reader X.
I removed the references in the registry, but did not remove the DLLs. I figured the Acrobat X installer would overwrite them.
I installed X, but found myself in the same looping crash. Looking at Add-Ins again, it was clear that the DLLs referenced for Reader were 11.x versions.
In the end, I found that the Reader X installer was not able to overwrite the XI DLLs. I manually removed them after taking ownership of the files. I then ran repair install of Reader X.