The 555 always has a greater than or equal to 50% output-high
duty cycle. In general automotive ignition uses a small dwell and
a long period between - no more current in the primary than is
needed to fully energize the core (short of saturation, barely).
This volt-seconds number, which is intrinsic to the transformer,
should determine your "on" time. Anything more is only wasted
(at best).
Since the parallel MOSFETs are showing you Cdg and/or Coss
sensitivity, I might suggest you look at RF LDMOS (if you can
find any at the kickback peak voltage rating) or maybe something
cute like a GeneSiC SJT (a silicon carbide quasi-BJT, real fast,
purportedly the lowest conduction losses in the wide bandgap
power device family, reliable past 300C including repetitive
avalanche - not that their 600V+ devices are likely to see
that, but you might be able to forego the power zener and
then not cut the crest off the flyback) simply substituted for
your present Darlington lower device.
I might also suggest that you change from a time and voltage
control mode (not that there looks to be any control per se)
to an emitter-current-terminated dwell - wait for the current
(across a low value sense resistor) to rise to a threshold that
suits the primary inductor saturation limits, snap it off at that
point, outwait the secondary spark extinction, and repeat -
a self-relaxation-oscillator, which might be as simple as a
sense resistor, a couple of common-emitter gain and timing
stages leading back to your Darlington base. I've sone this
as simply as a wirewound resistor and a 12V NC relay (but
with no regard to longevity - I expect the chatter arcing
would fry it eventually although a proper snubber might
extend that). At any rate the control ICs seem to be more
complexity than is warranted.