Most direct route for people traveling from CA to IL is the following:::
CA to NV to UT to CO to KS to MO to IL
I suggest that there is a good possibility that they took the body with them when they left. I think they may have taken the box out of the garage and stuck it into the back of the car, or even possibily if they had one of those old luggage carriers on top of the car. They made those back than. In order to avoid suspicion on themselves, they probably would have dumped the body in a different state.
Here's my thought. If you didn't tell anyone the child was missing, and than you moved away before anyone could ask, people would think at first you moved and took all of your children with you. Once the dad started asking questions they could blame it on a family member, by saying they left the child with someone. And now that someone is claiming it never happened.
Without a body being found, which is much harder to link to them if they dumped her body out of state, well no one has a case. Or at least not a good case.
My suggestion is we check each of these states for Does found anytime during or after the child supposedly died, which we have sometime in July of 1969. So that is a start.
Let's check out the records for the following areas first,
California (which I doubt I think they would have taken the body with them and dumped it good reason to get out of town huh? If you need to dump a body where no one will link it back to you)
Nevada --- I think Nevada may be very likely, bodies tend to start smelling after a time, and they may have wanted to get rid of her quick, or they may have thought it was too close to California for comfort and she may have been identified by her father if it was that close
Utah - Likely
Colorado --- Possibly
Kansas --- I don't think they would have kept her in the trunk that long perhaps but I don't think so
Missouri --- Maybe but doubtful
Illinois- Don't think so but you never know I mean odds are if they wanted her body nowhere close to them, they wouldn't dump her where they were now living. However, if the mother wanted to keep the body close by, wanted to bring flowers, (some sick parents kill their kids and feel the body needs to be close) welp could happen I guess