I'd like a reasonable list of laboratories where I could walk in, have
blood drawn, and then (some time later) receive (genomic) DNA
extracted from my blood.

Preferences are for labs (1) located in the US, (2) with demonstrated
proficiency in clinical specimen handling, tracking, and lack of
cross-contamination, (3) proficiency in genomic DNA extraction, (4)
not requiring any physician's, clinician's, or anyone else's
order/authorization beyond my own, (5) accepting direct payment (i.e.
not requiring health insurance coverage, reimbursement, or copayment),
(6) having a privacy policy in place to maximize genetic anonymity,
(7) and, potentially, offering secure DNA storage services and the
ability to send aliquots of my DNA to anyone upon my instruction.

And please feel free - in fact, encouraged - to add updated
information to this topic as a comment after the official answer
period has long past ...