The antique won't color the leather if you used the resist. All it does is stay in the deeper impressions. If you want it to color the leather you need to apply it without the resist.
I use the wooden mallet that came in the 'starter kit' I bought for the grandkids. I sanded it smooth and stained it. I use it sideways to 'press' pieces that have been cemented, and use the faces to tap stitching and lacing.
Your own dye will accentuate them the same way. If you can see it in undyed leather, you will see it when it's dyed. And while it IS a natural thing, it is NOT in/on all sides.
Goat is tougher, but still far too thin for footwear. I already gave you my preferences for moccasins. I've made, worn, hunted and danced in the moccasins I make for over 50 years. I do not think either of your choices are up to the task.
The only use I have found for veg tan sheep is lining holsters and other small projects. Sheep skin is too prone to tearing. It has no structural density. In plain terms, it's flimsy.
No, sheep doesn't have the density to hold up. And I don't know of ANY veg tan that has the flexibility for moccasins. Brain tan bison or moose would be my first choice. After that, chrome tan bison, elk or moose. Horse makes good moccasins as well.
I don't mind them, they add character, like scars and brands. But I won't pay top dollar for sides like that either. At $255, I'd send it back or demand a hefty discount. I'd also tell them that THEY can eat the shipping back.
You never want to 'slather' anything with NFO. I would clean it with a quality saddle soap, then if it is still dry, a very light wipe of NFO might be in order. Or a quality reconditioner.
As long as you do it the same EVERY time, your stitches will be consistent. As to the 'zig-zag' , 'saw tooth' effect, I've never had any of my stitching look like that in 30+ years.
I really like this finish from Bee Natural. I have used their line of products for years. From my work boots to my buckskins and most of my leather projects.
This particular one is quite similar to Fiebing's Leather Balm, but without the 'bubble' issue.
Leather Finish - 8oz (beenaturalleathercare.com)