I've started Hatari with TOS 4.04 in 68040 mode (68060 did not work
from the command line), then used the GUI to switch to 68060 and reset.
I've had a quick look at your new core again, and the problem, is movep:
Illegal instruction: 01c8 at 00E025E2 -> 00E0398C
with:
$e025e2 : 01c8 0000 movep.l d0,0(a0)
As far as I know, this instruction does not exist on 68060 anymore, and
it likely has been emualted by the old WinUAE core just by accident.
So I think it's "ok" if it crashes now. If we want to support 68060,
we've got to patch the corresponding parts of TOS.