BTW: This guy seems to have a 1260 with 040 CPU, as well.
http://www.amiga.org/forums/showthread.php?t=36906
he goes on to refer to it as a 1240 "They simply do not with the Blizzard 1240 (68040@40)... same configuration but... nothing!

"
He also calls it a 1240 in his signature:
"A500 +A600 +A1000 +A1200 +CDTV
A500 +K3.0 +Viper520CD +
A1200T +K3.1 +Blizzard 603+ (240/50) +
A1200T +K3.1 +Blizzard 1240/40 +
A1200 +K3.1 +Blizzard 1230/50+CoPro +
A2000 +K3.1 +A2630 +
A3000 +K3.1 +Cyberstorm MkIII +
A4000 +K3.1 +A3630 +
A4000T +K3.1 +A3640 + "
The 68060 has an extra row of pins, so the socket will need to be changed (although online it suggests you can bodge I and just add the extra pins). You need a voltage regulator and there is a suggestion that some resistors or diodes need moving/changing.
Someone was doing the mods professionally a while back, I wouldn't even begin to think about doing that myself.