I have a 31-15 and think it's great. There's tons of them out there and you can still get most of the parts you'd ever need.
I don't think you'll get a 135x17 to run as it's probably too long. I didn't try but I did a quick length comparison I think by the time you get the eye where you need it for hook timing you'll be crashing the needle clamp into the body at the top of the needle stroke. Here's a picture of the needles I run below. They are cheap and readily available on ebay. A suffix of LR indicates for leather.
I don't see a bobbin case or bobbins in your pics. I think it's a class 15. You should be able to get from ebay pretty easy. You just have to watch the little arm that comes off the case to keep from spinning, I had to trim mine shorter for it to fit.
If it was heavily used you'll probably have to replace the hook and the little pin you will find inside the tension assembly. If worn the hook won't run smooth, you'll be able to tell by the sound. Also check it for any burrs or sharp edges where the thread slides on it. The new ones I got on ebay have both needed some filing on the end opposite the hook to get them to fit. There needs to be a little play between the hook and hook driver to let the top thread pass. The little pin in the center of the tension assembly pushes the outer disc out a bit when the presser foot is up. They get shorter with wear and stop working all together when worn too. If your tension stays high when you lift the presser check this first.
I also agree on getting the smaller pulley on the motor, I run a 45 or 55 mm drive pulley. I also added a pulley the fits over the stock handwheel that increases the diameter to about 5.5 inches. That gets me down to as low as about 1 stitch per second.