Green Mountain has added a .40 caliber barrel to their "Gunsmith Special" section. I already snagged some .311 and .22 barrels from them.

They have a 20".40 blank now, for $33. But the twist is 1:16.

Looking through my loading data, I've found most ".40" calibers are .406, .411, or .421". The only standard .400" rifle cartridges I found were .400 Whelen and .40-65 Winchester.

That 1:16 twist sounds more like a .40-65 than a .400 Whelen. But a .40 bullet is likely to be short and fat by ordinary rifle standards; would the usual weight/twist charts apply?

Is there an already-tried wildcat that would work well with a .40, 1:16 barrel?

40 cal 1:16 twist makes me think of some sort of 'camp carbine' firing 10 mm auto pistol ammo.

As far as rifle cartridges to use that dimension barrel;
As I recall, the old .38-40 uses a .400" diameter bullet.

While there doesn't seem to be any 'established' cartridge/wildcat that takes .400 diameter bullets, you should be able to neckup .308 Winchester (7.62 x 51) brass to take a .400" or .401" diameter bullet and still have (barely) enough shoulder to use for headspacing. Since jacketed 40 S&W / 10 mm auto bullets work best at less than 1800 fps, a full size 308 Win case necked up should give you more than enough powder capacity.

That is all I think I know.

Piper106