Saturn rear-ended at low speed, but back still hurts

Any thoughts or comments about the following?

About six weeks ago, I (driving a '99 Saturn SL2) was rear-ended
while trying to leave a parking lot. I was stopped at a red light,
inched out a bit to see my way clear for a right turn, and the
driver who was stopped behind me (in a Dodge Grand Caravan)
apparently put her foot on the gas (!) instead of the brake.

The impact, from my POV, was very loud, sudden, and forceful --
definitely =not= a "love tap" -- and I felt like something had
pushed hard against the middle of my back, and that the wind had
been knocked out of me. I fully expected to find the rear end of
my Saturn reduced to a crumpled mess -- but, to my surprise, there
was almost no visible damage at all (just some deforming of the
plastic rear bumper cover).

Subsequent repairs (done by a body shop recommended to me by the
nearby Saturn retailer) came to roughly $800. The body shop
people said they had checked for other damage but found none.

I didn't hit anything (there was no car in front of me, and I was
not pushed out into traffic; I had my foot on the brake at the
instant of the collision, BTW). Thus, there was no front-end
damage at all, and the air bags did =not= go off.

I've had lower back pain ever since the accident. Not searing,
stabbing, intolerable pain, thankfully -- more like a very sore
feeling at, and below, my belt line. My doctor had it X-rayed,
but this revealed only normal degeneration (I'm 52). He says
it's probably a sprain of the lumbar region. I've been sent
to a physical therapy clinic; I've had one session (mild back
exercise, plus electrical stimulation and ice) and have been
prescribed six more (twice a week for the next three weeks).

Thankfully, I do not seem to have suffered any neck or head
injury. I was wearing my seat belt (I'm guessing that the "wind
knocked out of me" sensation may have been from my body being
thrown against the shoulder belt). I didn't lose consciousness,
and my head definitely did =not= whip forward or strike anything.

In case it matters any, I was rear-ended six years ago (more
forcefully than this time). Although it took quite a long time
for my back to heal from that incident, I did eventually get
better, and I was no longer having back pain by the time I was
rear-ended last month (i.e., the pain from this accident is
definitely =not= simply a continuation of pain from the earlier
accident).

The other driver's insurance company (Allstate) has admitted
liability for the collision -- it would of course be very hard
for them not to! -- but since there was so little damage to my
car, they're making noises to the effect that they intend to
treat my injury claim as a "minor impact case", involving only
minimal discomfort, and that they plan to agree only to a modest
reimbursement for doctor bills. (I have not yet made any demand
or agreed to any settlement for my injuries, BTW.)

Some questions:

Given that the impact apparently did not bend the frame or cause
significant damage (other than cosmetic damage) to my Saturn's
rear end, is there any way to do a rough guess of how fast the
Caravan might have been going when it hit me? (I know Saturns
are supposed to have 5-mph bumpers, but does that necessarily
mean that a collision faster than 5 mph =will= result in damage
to more than just the bumper?)

The body shop (supposed to be a very good shop, and recommended
to me by the nearby Saturn dealer's service department after I
expressed concern that I wanted to be very sure my car would be
repaired right) insisted there was no frame or body damage. I'd
assume that they're probably right -- if by any chance they were
dishonest or incompetent, I'd imagine they'd be more inclined to
claim there was more damage rather than less -- and the car does
appear to handle just fine as far as I can tell -- but is there
any reasonable way to confirm that my vehicle really is (or is
not) fine?

Has anyone else out there had long-lasting lower back injury
from what appeared to be a minor, slow-speed rear-end collision?
How long did it take for your back to heal? What did you have
to do to get long-term relief from the pain? Were you able to
get the other person's insurance company to believe the true
extent of your injury and give you a proper settlement, and if
so, how did you do it?

Rich Wales http://www.richw.org