Er...I am so tired but somehow slowed down to thinking more clearly. The driver I'm running now is obviously 64-bit, otherwise it wouldn't work with the 64-bit kernel (without booting into 32-bit kernel mode). I guess what I was remembering is that the driver installer is probably 32-bit (without checking), and wouldn't work. It installs either 32- or 64-bit drivers, as the release notes says it's compatible with both. So, even if the installer is 32-bit, I suppose you could install the 64-bit kext manually.
Also, I'm viewing this with the new Mac Pro in mind, since my old one would would need a new graphics card at minimum to support Catalina. So either way I was thinking to be at the end of the line with firewire (though I guess I could go thunderbolt to firewire cheaply...).
However, all the associated applications are 32-bit, and will not work under Catalina, hence my comment about keeping a VM around with High Sierra or something.
So, it looks like maybe $29 firewire-TB adapter and hope the pieces work together, or $105 lightpipe-USB adapter requiring no driver.
PS—kexts—kernel extensions—are something to avoid if possible in the transition and in the future, there are a bunch of caveats with Catalina and going forward...