I've gotten an email reply (I've been asking technical support as well as this forum) and a preliminary test indicates that things seem to be fixed (I patched one keyword test successfully). I'm just wondering what is the "right way" to do things in TC.
Earlier I tried to patch the recorded tests by making every initial "Navigate" browser step use a "Code Expression". That "Code Expression" uses the Project variable I setup for our domain (which changes) and the portions that don't change (for instance the page itself...).
What I found was that the keyword tests failed on a large number of "Object Not Found" errors because items that I thought were subordinate (and assumed would automatically change), had the URL hardcoded into them (with the original domain value).
Finally, tech support suggested changing all those hardcoded URLs (which I wanted to change into "Code Expression"s) to use a wildcard in place of the domain name. So now I have both the "Navigate" step using a "Code Expression", and in "Name Mapping" I have subordinate objects using a wildcard. I'm wondering if this two part approach is what is generally suggested in TC in this case. Also, how does the system know what to use for the wildcard (I didn't tell it which domain to point to on those hardcoded steps, but somehow it seems to point to the right one).