Archie, I'm sure we'd all love to see photos of your bike!
Unfortunately, I haven't any - the only salvaged part I've got is the saddle... But I surely can post pictures of other people' bikes!
I think you don't want tension, as such, on the leather. Tighten the nut only enough to take up all the slack, so it doesn't rattle. If you put actual tension on the leather, it will tear at the rivets. I had a nice Brooks Pro that I (or someone) ruined this way. I got it used (but pretty new) and may have tightened the nut at some point between 1980 and 1985, and tears started appearing in the mid 90's; took a while, but clearly the leather was under too much tension.
Thanks for warning! Of course I don't intend to put excessive stress, but as I understand, riding the saddle will apply the tensioning force anyway - so my only hope is, that leather isn't damaged by dry rot or similar things, and will withstand it...