Are you sure your cat con is OK?

In my case the indy probed the exhaust upstream of the main cat con at the oxygen sensor location (420ppm HC) then at the tail pipe (320ppm HC) which told us the cat con was defective.

After replacing the (smashed) cat con, tailpipe reading came down to 11ppm! We did replace one of the two pre-cats (this was a 1981 M116 380SLC - your M117 560SEL s/b similar) as it came attached to the main cat, but it's the latter that does most of the work.

That was after I did all the work on the induction system which fixed the rough idle. After all that the idle was dead smooth but you could smell the gas at the tailpipe - didn't even have to consult my dog on that one....

I do like your thinking - UT is so pristine, especially around Bryce and Zion, that every bit helps.