Some years ago, a friend & I were prowling the back country with a 351 and 401.  We found a burned down cabin with about half of the brick chimney still standing.  The rest of the bricks were scattered around.  We found that we could hit bricks at 35 to 50 yards, most of the time.  That level of "accuracy" even worked when shooting factory 357s with the rim turned down in a drill press.  The 351 shattered the bricks.  It is a more powerful cartridge than the 357.  The 401 absolutely vaporized the bricks.  But I don't think either rifle is capable of accuracy better than "bricks at 50 yards".

When I was in high school back in upstate NY, I saw more than a few of the M-1905 blowbacks converted from 32 WSL to .30 Carbine.  That gave you a rifle that was about the same size as the GI Carbine but one that weighed twice as much.  Anyhow, you could get ammo for it, which is more than you can say for the rest of the WSL series.

Campbell's Winchester Single Shot book shows a High Wall chambered for .351 and another in .401.

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This is excellent advice. I have most of the Ideal manuals and the old books written about reloading. With pre-war loads you have the dual problem of changes in the burning rate of powder plus larger capacity balloon head shells. Post war powders have also changed. Now that Hodgdon has bought most of the powder companies, I would suggest sticking to their suggested loads that are offered free of charge on their website.