Turns out satisfying ICE38 by making a registry key the keypath is wrong. The proper thing to do is to ignore the ICE38 error but going going into the wix properties page and add ICE38 and ICE91 beside "Suppress specific ICE validation.
Microsoft or Wix doesn't have ideal support for pure per-user installs. I couldn't even find any good examples online.
Bryan at WiX-users@lists.sourceforge.net helped me out on this:
Since that is the case, ICE38 is (in my opinion) incorrect and you will want to ignore it. ICE38 implies you are installing per-user resources in the context of a per-machine installation but never verifies that this is so.
Actually authoring a per-user install requires that you ignore ICE38 because it won't ever be accurate for that world.
Once I ignored that the above worked.
[Edit]
See my answer here as well. Turns out there is some edge cases you need to be aware of.