I think that the .223 WSSM was a highly over-driven cartridge right from the drawing board. Winchester was wanting to get .220 Swift velocities from it, and that's how they marketed it.
I would say, however, that you could get the cartridge to shoot well with 60 grain bullets, if you use a slower powder and slow the bullets down...
I think the cartridge would work--there's no actual reason that it won't. You can load it long and compensate for a certain amount of throat erosion which may have already occurred (if it's a used rifle)... or, if the lands are not reachable with the 60 grain bullets, don't worry about that--just seat them a caliber's depth into the case and go with that OAL. Many factory loads shoot really well with deeper seated bullets, and there are actually some reasons why seating the thin jacketed varmint bullets deep might make them work better. Look at Hornady's excellent factory varmint loads--see how well they shoot, but see also how deep they seat the bullets.
By going with a slower powder such as 4831, and keeping the charges near the published starting levels, you could mitigate most of the troubles this cartridge has had in the accuracy department--not to mention preserve the barrel for a longer time to come.
The WSSM brass is often nickel plated, and that can be a problem, as the flecks of nickel get into the case mouths and create runout from hades, so be sure to burnish out those case necks with some steel wool spun around an old bore brush, chucked in your cordless drill. You want smooth, clean brass in there, and nice chamfered necks...
With 60 grain bullets, try some 4831 between 41 and 43 grains, moving up in .3 grain increments, and you'll probably find a reasonably accurate load making around 3200 to 3400 fps. The 4831 works great in over-bore cartridge designs, and you get plenty of case fill without shooting up the pressure. The reason that Hodgdon didn't test 4831 is that it would not produce the velocity that this cartridge was initially acclaimed for. But it will work--start it out at 41 grains and work up from there with the 60's and you'll get velocity between .223 and 22-250, and decent accuracy I'm betting.
Dan