Hello Vermonter across the Connecticut River!
Stitching up leather on bars is not difficult. Over the winter I made my own (along with hoods for Dura Ace AX levers) from goatskin and below are the results. I did not use
rhm 's great advice above to pre-stich a tube and slide it over the bar end loose before tightening. I actually sewed mine directly to the bar and then came back and sewed on the lever hoods. The top photo shows the hood in an earlier variation. The bottom photo shows the hoods in their final form with all the stitching in place.
There are several different styles of stitching you can use. Probably the most popular is the baseball stitch (which as you can see I did not use). You can find many YouTube videos describing how sew this common and other stitches.
The key is to stretch the leather into place for a good fit. Since your leather is already (and has been for many decades) pre-stretched, I'd be conservative on using any kind of conditioner on the leather.
Best of luck on your project and IMO your saddle looks just fine!