Hermann Oak has a minimum of ten sides or backs of one thickness.
http://www.hermannoakleather.com/products-and-pricing/tooling-and-carving-20110204130556
Try some Kidskin from Springfield. It's 2 oz. I've used it for the entire interior of wallets.
It's reasonably priced and there are lots of colors to choose from.
In the end it's a matter of personal preference & skill but in general a stitching 'chisel' is meant to punch all the way through and the pricking irons are meant to just mark stitches and be finished with an awl. I've done both but I am moving toward just marking with my Blanchard irons now so I can make the holes as small as possible with an awl and still get the needle & thread through. I think this ends up being stronger and looking nicer because of the smaller holes in the leather.
In my opinion your .8mm Tiger thread will be too big for the 9 TPI Blanchard that you have coming. I use 632 Lin Cable for 9 TPI. You could also try the 632 Amy Roke thread.
A few suggestions to create a higher end look on the iPhone clutch:
Don't bevel the edges; instead paint the edges with several coats and sand with a fine grit and buff with paraffin wax.
A small crease around your edges will give it a more finished look.
Back stitch 2-3 stitches. That's it. Maybe a touch of glue.
Make sure your final 2-3 holes are as small as you can make and still get a needle through.
I 2nd the Buckle Guy suggestion above. https://www.buckleguy.com
They used to have some black items and still have some Gun Metal color. They might be able to do special orders.
Chèvre Chagrin and the others you mentioned might be a little pricey for practicing on.
Try Maverick Leather for some Horween 2nds.
Springfield Leather has some goat, kidskin and pig that is nice looking but not too high for practicing on.
John James needles
Vergez Blanchard awls and pricking irons
https://www.rmleathersupply.com
http://www.fineleatherworking.com
Check out The Leatherworking Handbook by Valerie Michael. She doesn't hit on watch bands but the she covers enough to get you going.
I've been using the Tandy edge paddle for a while now. Best tool I ever bought at Tandy. I use it with Fenice edge paint.
https://www.tandyleather.com/en/product/craftool-stainless-steel-edge-paddle