Reddit mentions of Stanley 12-951 SpokeShave with Flat Base

Like this one? It's a little fiddly to adjust but works great once set up. If the cap's threads are stripped you could drill & tap for a larger screw. But seeing as how you have a Veritas set there's not much point in futzing with the old one... I'd give it away.

Stanley spoke shave works great and under $20. You've got enough meat on that handle that you can practice and get the blade right.

Stanley 12-951 SpokeShave... https://www.amazon.com/dp/B00002X1ZG?ref=yo_pop_ma_swf

Then use your rasp there to clean it up and get things rounded off better. Finally moving to some sandpaper.

Awesome job, really excellent for the first couple. My first couple were dreadfully unbalanced and unequal. I personally like a spokeshave to do handles, as you can control depth of cut very easily so you don't accidentally gouge too deep or start getting too thin. It also allows you to get very even and symmetrical contours on the handle and outside bowl. This Stanley one works well but you can get cheaper version on Amazon and eBay. I started out with a cheaper one but the steel isn't great quality and the mouth is a bit too big, but it will work well enough just starting out and investing in tools. If you have any antique shops or flea markets around, check those for old antique spokeshaves. Some may need refinishing but that is a fun hobby in and of itself. It you can find an old Stanley #53 adjustable mouth spokeshave, they work the best in my opinion because you can tune them to take extremely thin shavings and the surface is left finish ready. It is just my preference, it can all be done with carving knives with enough practice. I prefer the bench vise and bench tools method more than carving knives, mostly because I work in seasoned hardwoods instead of greenwood.

The "live" backing helps a lot with that, its also just nice aesthetically. I will try to post a pic of one of the ones I did.

What tools are you working it with? If your not going for the 100% authentic survival tools I recommend a tool called a spoke shave.

Very useful for slowly removing material, you can generally find them very cheap at antique shops or used tool stores, they can be a little tricky to adjust and sharpen but they are simple enough mechanically.

Otherwise thick broken glass (wine bottles work well) makes a great scraper.