Found it!
To avoid clogging up the backup with clw's, map's, lib's obj's and other files that are easily regenerated, my .red file says:
*.* =c:\Cstuff;.; %ROOT%\libsrc; %ROOT%\images; %ROOT%\template; %ROOT%\examples; %ROOT%\convsrc;%ROOT%\CPCS600;%ROOT%\CPCS600\IMAGES; C:\Clarion6\3rdParty\LibSrc
and the .bat files, both of them, land there. I think they don't run when the template tries.
So I added *.bat = .\ to my red file and the bat file runs and copies files and the gzip gzips.
It still always thinks the web folder is out of date, but it does its work, I think.