The 12AT7 has a tapped heater which can b used at either 12 volts or 6 volts. Stereomour II has only a 6 volt winding on the power transformer, and the 12SN7 has only a 12 volt heater. So you could use 6SN7s, but not 12SN7s. You could of course use a voltage doubler to get 12 volts DC, but you're on your own to design it - and figure out where to put it. edit: untrue
Even if you did use 6SN7s with AC heaters, you'd still have to cut a larger hole for the larger sockets, and figure out how to wire the 12SN7 6SN7s. The gain would drop to 1/3 of the original, in most cases requiring a preamp and thus rendering the volume/balance controls redundant. And of course many of the resistors in the driver and C4S modules would have to be replaced with different values to accommodate the different tube parameters. All in all, a fairly significant amount of work!