Thanks to all, I really appreciate the feedback.
ALterEgos response was most helpful. My original numbers were with ACR Process 2011. I ran conversions again using Process 2010, using the defaults (Blacks 5, Brightness +50, Contrast +25). That gave much lower Delta-E values, but strangely a much higher difference on the BasicColor profile.
BasicColor Profile... Delta-E = 6.30
DNGPE Profile........ Delta-E = 4.17
DcamProf Profile..... Delta-E = 4.46
AdobeStd Profile..... Delta-E = 4.26
My goal, I think, is to have a profile that produces the most accurate colors, not necessarily the most pleasing. It seems more reasonable to me to get from accurate to pleasing via adjustments than to start with inaccurate. Plus, old age and an eye injury have lowered my trust in my visual judgement. So I'm moving more and more to evaluations "by-the-numbers". My goal here is also to simply advance my understanding of the process. I have no intention of spending $500+ on BasicColor, and can't imagine what it would take to justify that cost.
I understand that perfectly matching the LAB reference numbers of the ColorChecker is unreasonable. It's just not possible for the average shooter to match the exact same D50 lighting conditions and exposure. But it's starting to seem reasonable to use the difference between Delta-E values to help judge the quality of profiles compared to each other.
I've followed several debates about how best to shoot a ColorChecker target for use in profiling. Even lighting, avoiding glare, and avoiding color reflections are the center of most of those debates. But there is little discussion of the best exposure to use.
Most guides just say use ETTR and avoid clipping on either end. In one old discussion, Eric Chan said the white square should have a Lab-L value of 96. The MacBeth reference values show Lab-96. The BasicColor documentation hints at the same.
However, I've shot the CC24 with bracketing that yields Lab-L values between 89 and 98. When I feed those shots to DNGPE and Xrite software, I get significant differences in the resulting profiles. Basically, the higher the exposure the higher the saturation. Hues don't shift much, but saturation does. An L96 profile can easily push saturation beyond the limits of Adobe98, while an L89 profile leaves room to spare.
Now I notice that my DNGPE profiles made from a LAB-L 96 shot generate larger Delta-E values than a profile made from a Lab-L 92 shot. However, the BasicColor profiles I've generated from different exposures do not show a significant difference. They are virtually identical. A mystery to me.