EDIT: I'm just going to accept my own answer, as it did solve one part of the problem for me. If someone posts something more like --bind in Linux, I'll accept that answer.
In an effort to spur more answers, I'll begin answering my own question with what I have found out.
Step 1 is to get a ramdisk mounted at boot every time. To do this, I create a bash script and then a launchd entry to call the bash script on boot.
Write a bash script like this:
if [ ! -e "/Volumes/$RD" ]; then
diskutil erasevolume HFS+ "$RD" `hdiutil attach -nomount`
mkdir -p /Volumes/$RD/private/tmp
mkdir -p /Volumes/$RD/private/var/log
mkdir -p /Volumes/$RD/private/var/tmp
Then get it called on boot by adding it to launchd by creating a file called /Library/LaunchDaemons/com.my.ramdisk.plist with the following contents:
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
Where I am stuck is a way to symlink or mount directories inside the ramdisk at /tmp, /var/log, and /var/tmp. These three directories are all symlinked on my system to /private/tmp, /private/var/log and /private/var/tmp. When I changed the symlinks to point into /Volumes/ramdisk/..., the system won't boot. I expect this is because at boot time, something wants /tmp and /var/log BEFORE the my com.my.ramdisk script mounts the ramdisk. I need a way to mount the ramdisk right after root is mounted, before anything else runs.