On Sunday, February 15, 2015 at 9:08:03 PM UTC-8, mike wrote:

the main component of the
primary current is due to the shorted secondary.

** The secondary is not shorted.

My thinking was that, if not for saturation, the SCR would be less
stressed if I turned it on at zero voltage when the primary current was
zero. And from the unpowered state, the voltage and current can't
be anything but zero.

So, this is a concern that the SCR's dI/dt rating may be exceeded
if peak voltage is present at the turnon time (the specific
microsecond of time, because SCRs turn on faster than
an AC period). That's a valid concern, with two solutions:
(1) use an IGBT instead of SCR (yeah, I know, it's a big deal),
or (2) use a transformer with enough stray inductance that
the worst-case current risetime is tolerable.
One hopes that the transformer is appropriate to this kind of
frequent-switching use, and fulfills requirement (2). You
really HAVE to hope, the microsecond-scale inductance of
the transformer cannot be easily measured (the core isn't
fully magnetized that quickly, so 60 Hz measurement tells
an inappropriate value). Flux coupling to the secondary
will also be poor for that short time.

A 'typical' SCR (TYN640, in stock at DigiKey, needs dI/dt under
50A per microsecond...) doesn't need much inductance to keep its
turnon conditions satisfied.

And that, if I could arrange the resting place on the B-H curve
from the previous pulse such that the first half-cycle wouldn't
saturate the core...

Again, this depends on the transformer design and material. Remember Phil's
comment that a 240V transformer on 120V excitation wouldn't saturate-
because a 240V transformer has an oversize core for 120V excitation.
The key concept is that the core remanent field also might be zero,
and a first half-cycle starting at zero magnetization is more stressful than
that same half-cycle starting at the inverse remanent field (which is what
subsequent cycles of AC excitation provides). Starting at peak V
is a safe bet if the remanent field is negligible, like when
the gadget has been powered down for a while.