For anyone who cares, I figured I'd fill in with my latest info.

In my earlier response I had described how I converted a Slackware distro to
a "multilib" distro, which was not a standard 64-bit installation. A "multilib"
distro has both runtime libraries (.so files) and development libraries (.so
and .a archive files) installed. It turns out that /lib is where 32 bit stuff
goes and /lib64 the expected standard for the 64-bit kernel. For those who do
not know, runtime library paths are taken care of by ld.so (you can look it
up). For Slackware, "alien Bob's" packaged libraries and scripts take care of
the multilib part.

I first tried it in a VDI dual-boot VM in VirtualBox. Then I tried it on a
real system, the "/" root filesystem of which I had cloned with "rsync" to a
new partition (booting was done with GRUB by having added to the grub.conf an
having modified the / mount-point in /etc/fstab in the new partition). This
worked very well.

I built WINE on the real system. There can be a misconception here. A very
standard WINE build is meant to run 32-bit apps. So, one needs to get the
64-bit build with './configure --prefix=..... --enable-win64' and then make it.
Online instructions (including the WineHQ.org wiki) on how to proceed differ
and conflict. I would say they are outdated. The claim is that ones the wine64
is built and installed one needs to build the 32-bit one, like this:
'./configure --prefix=..... --with-wine64=BUILD_PATH' and BUILD_PATH has to
be the directory where 64-bit build took place, say ~/builds/wine-2.0.1/ or
something similar. This did not work. People online have suggested jailing
the build to a 32-bit container, something I did not do. I just built the 32bit
WINE and installed to a different place.

I use environment modules to manage the runtime side of WINE as with other
software. I built one module for WINE 32-bit ("Wine32") and one for the 64-bit
("Wine"). I 'module load Wine32' to get the environment ready to run on 32-bit.
The only caveat is that the ~/.wine directory will not be compatible across
the 64-bit and 32-bit WINE builds. I have two of those now and a sym-link to
~/.wine is needed every time I want to run something specific. The real problem
is if I wanted to run simultanuously a 64-bit Windows executable and another
32-bit one. This is not a concern at the moment given what I want to do.

And one last piece of info to ensure that this thing works and that WINE (and
the work that people like Codeweavers are doing) is great is this: I managed to
install and successfully run a music sequencer and its plugins, Fl Studio from
ImageLine Software (versions 10 and 12) which was my motivating goal.
https://appdb.winehq.org/objectManager.php?sClass=application&iId=178

This last part.... Wow! Linux!