The best bullet style, diameter(s), length, weight, etc. can be determined by the twist of your barrel (breech & muzzle), groove diameter and leade.
The .32-40 RKS barrel on my bench rest Ballard has a long leade (half degree included) and I get very good accuracy using the bullet shown below. BUT that's my barrel which is .321 at breech, twist of 1:21 at breech and 1:11.5 at muzzle.
If not for the extreme leade, that bullet could not be breech seated. Sure works great in my barrel though.

The 205 grain bullet is excellent for the gain twists ending at 14:1 but for my gain twist finishing at 11.5:1 twist it loves a 236 grain bullet. 
That Brooks diagram looks fairly similar to the old Paul Jones Spitzer. 
Most of the .32-40s were made finishing at 14:1 unless the owner requested the tighter twist.

I have had a number of Ron's .32 barrels and have always shot Paul Jones or Barnett .323 diameter (on all bands)  spitzer bullets in the .321 groove-to-groove barrels with great accuracy using 20:1 alloy.

I never had anything happen with my RKS .32 barrel. I started with tapered Pope bullets at 202 grains and it shot bug hole groups. Then I used tapered Ron Long spitzers at about the same weight and it shot bug hole groups. Then I switched to Barnet style bullets out of a Andella mold and it still shot bug hole groups. Then I used Paul Jones 220 grain tapered bullets and it shot bug hole groups and scored a couple 250s along the way. At Ogden it was hot and dry and got some leading with the Paul Jones. That was perty exciting... So now I use the Barnet style bullets because they look more accurate. It doesn't matter what bullet I shoot in it. No surprises.   

There was a definite lack of a feeling of accomplishment with my RKS barrel. No hours and hours of testing and head scratching.  Now I got this .38 RKS barrel that shoots bug hole groups....  Good luck Flatlander but you may not need much.

I thought you and the family were down with Covid? Glad you have enough strenth to do some typing, big guy.
Our bugs are big but not that big. 

Do you have a rifle with an RKS barrel on it? I know you did. It was Bevs old carbine HW. I mean one that shoots bug hole groups.

I assume the Lyman "French" bullet should work. I also have a Wayne Vietz spitzer mold around somewhere. Has anyone tried Pope style flat nose bullets? Hoping to not have to purchase yet another new mold for this project. I know I should just load and try and see what target says  but with large rifle primers at premium I hate to waste them on starting testing without direction to go.
Flatlander

I had a Ruger #1 with an 8 groove RKS barrel and it shot the Hoch 322200D bullet very well.  The "D" designation was for Douglas barrels I believe.   

Chris.

This is a direct copy I did for NOE of a PJ mold, designed for the 12 -11.5 twist RKS barrel (Note the ELCO in the address).

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This is the same mold, for a 14 twist barrel but, it's only available, right now, in 4 & 5 cavity.

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