> I'm still stuck on getting the right name to show up in ARP.

It may that indeed Installer blocks the property from being passed onto
the server side. Three things to try:
- inspect the log file, to see whether it is passed, and then whether it
  gets set. You do logging with "msiexec /i foo.msi /l*v foo.log".
- add the property to SecureCustomProperties, to have it passed to
  server mode; by default, only properties in UPPER_CASE get passed.
- alternatively, add an upper-case property, and make ProductName
  computed.

> Another problem: it seems like we have to update the ProductCode at
> runtime as well

I knew that would cause problems some day :-) I expected you to desire
this only for a single installation. Installing multiple copies is much
more difficult.

IIUC, a common approach is to use transforms, although I'm not sure how
precisely that would work.

A hacky approach might be to use computed uuids (if that can work at
all: I'm skeptical that you can change the productcode at runtime):
have a fixed ProductCode in the MSI, and then add the minor Python
version to the last digit of uuid. See Tools/msi/msi.py for how the
uuid of the Win64 installer changes from the one for the 32-bit
installer.

I think this is really is a question to ask on some MSI channels;
most likely, the answer is that this cannot possibly work.