I set up my test NFS server and built a PXE image, following the lead of the FreeBSD handbook, and a PXE setup that we use at $work. After getting my virtual PXE host to boot, I quickly discovered that I was unable to login as root, despite having set a password. After a lot of screwing around, including compiling 3 different FreeBSD source trees, I finally tried booting with the memory filesystems, as described in section 32.8.2 of the handbook. This allowed me to log in, but was still not ideal, since changing anything in /etc required rebuilding the archive. I was also unable to shut down the PXE VM, because calling shutdown returned "permission denied," as root.
Turning to smarter people on IRC, it was suggested that this behavior is usually seen in FreeBSD jails, a nosuid-mounted filesystem, or incorrect permissions on /sbin/shutdown. The second possibility got me to thinking, which led me to the answer. My NFS export on the server was missing the '-maproot=root:' directive. Adding this directive got everything working as expected.