Then you're looking in the wrong places. Try an antique mall.

American made axes from the golden age were routinely 56-58 Rc at the edge, and I have a couple that I could swear are at least 59-60, if not more. Only one of my vintage Americans has an edge that I'd estimate to be around 54-55.
And of course, they were all using plain carbon steel of some kind. So if a 10XX steel does the job, then I'd be looking toward getting the edge harder without sacrificing impact toughness. Maybe try to push for 61-62 Rc. Which alloy has the best impact resistance in that range? The geometry lends a lot of support to prevent gross damage, but the very edge can get rolled much easier. Wear resistance is not a factor in a tool like this, as far as I'm concerned. That's not how the edge degrades in normal use, and even if it does, that sort of wear can be fixed in seconds with 3 passes per side on a fine hone.
I like the suggestions of L6, 5160, and don't rule out S5 (which can obtain much higher hardness than S7 but still has crazy toughness), or other silicon alloys. Also check out the "chipper steels"- used for making blades that chip wood into pulp in mills; it seems like they should be basically engineered exactly for this application.