Maybe ask your question again at the end of this thread:
It sounds like the Cubase normalize is peak normalize, but I’m not sure. You can try it and see if it gets close enough for you. You might have to check and manually adjust after any of these processes anyway.
You could get Wavelab Elements, load all your files in a montage and use the loudness normalizer (which is non-destructive), but like I said it seems you would have to manually mark and manually export each region individually after normalize.
Wavelab full version would be easier.
If this is a one time thing, there are probably other programs that do this specifically, converting with replaygain, but Wavelab is a great program and well worth having for other things. Elements might be fine, try a demo. fwiw, I’d buy direct from Steinberg. Ebay might be getting better, but my experience has been they simply can’t police each and every software sale.