My brother, and his friend, Phil Quaglino, are the .40 caliber shooters I know, and really KNOW the round well. So, I called him and sent your question to him. After talking to Phil, he noted that there are two main problems with shooting Conicals in a .40 caliber ML rifle:
1. The greenhill formula still applies, and if you have a 1:48 ROT in the barrel you bullet needs to be only 1.5 times the diameter of the bore, or about 6 tenths of an inch long to stabilize. That leaves you shooting pistol bullets, mainly those for the .38-40.
2. Groove depth. On ML rifles, the grooves are much deeper, so you can shoot a PRB. The grooves are at least twice as deep as what is normally put in a barrel designed to shoot bullets. That causes problems in keeping the gases from cutting and melting the bullet before it escapes the muzzle of your barrel!
Phil has a fast twist barrel with a 1:16 ROT. He is shooting a 305 grain round nose cast bullet, designed for the .40-65 rifle. The grooves are also shallower, designed for shooting cast bullets, rather than the PRB.
Phil also shoots PRB .40s, with the deeper grooves, and PRBs, but he doesn't try to shoot the conicals in them.
However, T/C was selling a " Mini Ball" in .40 caliber similar to one made and sold by Rush Creek Roundball.1-877-674-4949; or 1-877-674-4947. Phil sizes these bullets back down to .400 and loads them in his .401" bore. The sizing dies can be bought for about $20.00.
Rapine molds also offers .40 caliber pistol bullets, and rifle bullets, in varying weights and sizes. I have not checked with RCBS, but they may also have such bullet molds. Lee has a couple of molds for 40 caliber. Most of the pistol bullets are in the 175-185 grain weight, but they are short enough that they will stabilize in the 1:48 ROT barrels.
As for sealing gases, I recommend using an OP wad, and then even add a coarse filler, like Corn Meal on top of the OP wad to push the bullet down the barrel. The meal will fill any gaps in the deep grooves that the OP wad can't reach, but the OP wad is stronger and will do a better job of holding back most of the gas. The problem will always be that deep- usually square bottom-- groove depth. If the bullets are cast from soft lead, or pure lead( My brother bought some 20:1, Lead to tin alloy lead from John Walters of Walter's Fiber Wads, in Oklahoma, that turn out beautiful bullets for his .45-70 ) the bullet should be expected to " bump up", or "obturate" enough to take the spin of the rifling.
I think the key to successful accuracy with .40 caliber conicals is to be careful how long a bullet you choose for the ROT, sticking with that 1.5 times the bore diameter. These pistol bullets mentioned, the Rapine 40175, and 401180 are about .66" long, but should be stabilized with that fast twist rifling.
Then keep the velocities within reason. The better Ballistic's Coefficient and the elongated shape of any conical will drive that bullet much deeper than any PRB, so you don't have to worry about depth of penetration, even at modest velocities. With the bullet sized to your bore diameter, it should slide down the barrel easily, and then you only have to decide if you want to put an OS card down on the bullet to keep it in its position against the OP wad and fillers. On a target range, the OS card would not be necessary. Hunting, it might be a good idea.
If your muzzle is coned, you might actually want to try sizing the bullets .001" OVER bore diameter, so you have to score the bullets on the lands to drive them down the barrel. That would help keep them straight, and obviate any need for a false muzzle.
I have not checked the Cowboy Action ammunition suppliers, but the .38-40, as well as some of the newer .40, and .41 caliber pistol rounds have come back in favor, and there probably are sources of bullets for reloaders in those sports.
YOu might also call Eddie May and ask him what he has, or can cast for you. Peter tells me that he has talked to Tony Vance, the owner of Rush Creek Roundballs, and Tony told him he bought out the casting tools and molds from a man who retired, and he has dozens, if not hundreds, of molds he still has not examined or catalogued. So, talk to these guys directly about what you need. I bet they will be willing to cast up a reasonable order.