Further reading brings up these statements:

Three phase operation. Only special order Models KS-1027, KS-1227,
KM-1027 and KM-1227 will operate on a three-phase supply. However, any
Skutt kiln can be properly powered via unbalanced connection to two of
the three hot wires of a three-phase supply. Of course, the green safety
ground connection provided in all Skutt power cords is also used.

Three-phase installation. Three-phase models KS-1027, KS-1227, KM-1027
and KM-1227 can be plugged directly into a three-phase (15-50OR) wall
receptacle.

208 versus 240 supplies. As you can see from the chart, most Skutt
models are available in either 208 or 240 volt versions. The exceptions
are models KS-714 and KM-714 which are universal, and will fire with
240V or 208V power. The "120/208V" supply is increasingly encountered in
schools and newly built communities, because it is more efficient for
heavy 120V loads. This affects models KS-818, KS-818WR, KS-1018,
KS-1027, KS-1227, KM-818, KM-818-30A-3, KM-1018, KM-1027 and KM-1227
because their elements receive the full 208 *or 240) applied volts. The
208V versions should never be fired on a 240V supply without first
installing a full set of 240V elements. Otherwise, all components will
be seriously over-taxed.


RoyJ wrote:
And 60 seconds on google comes up with the wiring diagram for the 3
Model 1227
http://www.skutt.com/pdf/service_man..._km12273ph.pdf

and the single phase version:
http://www.skutt.com/pdf/service_man...m1227-1027.pdf

The only difference is the main terminal block, the wiring from the
terminal block to the relays, and the main power cord. All the elements
are rated 208/240 with no derating in power. Note that the power rating
for the 240 single phase version is 48 amps with a 60 amp breaker.
http://www.skutt.com/support/elec_req.html

The OP does not sound like the type who can handle heavy power wiring
but I'm sure the local pottery place could do this in an hour or so. Any
high end pottery supply place has a tech that relines and rewires kilns
on a daily basis. They also do the upgrades to add more sophisticated
controls, the power wiring is just a small part of that.