Linux kernel dropping custom keyboard scan codes

You're making several wrong assumptions: that X ignores udev (it doesn't); that udev directly intervenes in keyboard mappings (it only sets them up, beyond that it's the kernel acting); that X is based on Linux (it runs on other unix variants as well).

Udev only plays a very limited role in keyboard handling: it detects specific keyboard models and declares their vendor-specific keys. Udev doesn't act on standard keys like A and F1, only on vendor-specific keys like Brightness up or Wifi on/off (usually marked by icons). These keys are typically not used by application, but mapped to ACPI events.

The Linux kernel has its own mapping scheme for the usual keys, which you can set with the loadkeys command. If you have multiple keyboards plugged in, the settings performed by udev are specific to one keyboard, whereas loadkeys acts on the global kernel keymap.

The kernel's keyboard mappings don't cover nearly all the nuances afforded by X. So X has its own scheme and for the most part ignores kernel settings. X does take the keyboard-specific mappings set up through udev into account.

At least in my case, the problem was that the address needs to be in lower case! So, in your case, change ATTRS{address}=="00:1F:20:76:41:30" to the following:

ATTRS{address}=="00:1f:20:76:41:30"

In case that doesn't do it, I'd double check the permissions.

Also, udev should set a DEVNAME variable (among others) which you can use, so you don't really need the grep the logs (another possible candidate for a permission issue). To troubleshoot further, you could just create a log file every time the script is run (from the script) - that way, you will know if the script was run at all - i.e. if the udev rule triggered at all, or if the error is somewhere later on.

So, the authors script solution (on the page you have already linked) is better IMO. I've adapted it as such:

Permissions:

# ls -l /etc/udev/rules.d/50-k810.rules /opt/bin/k810*
-rw-r--r-- 1 root root   106 2014-07-16 19:21 /etc/udev/rules.d/50-k810.rules
-rwxr-xr-x 1 root root   304 2014-07-16 19:39 /opt/bin/k810.sh
-rwxr-xr-x 1 root root 13102 2014-06-07 22:05 /opt/bin/k810_conf

50-k810.rules:

KERNEL=="hidraw*", SUBSYSTEM=="hidraw", ATTRS{address}=="my:k8:10:ad:re:ss" \
 RUN+="/opt/bin/k810.sh %p"

k810.sh:

#!/bin/sh
LOGFILE=/tmp/logfilek810sh.log
echo "RUN: at `date` by `whoami` act $ACTION \$1 $1 DEVPATH $DEVPATH DEVNAME $DEVNAME" >> ${LOGFILE}
echo "Setting F-keys on for your K810!"

if [ "$ACTION" == "add" ];
then
    # configure k810 ($DEVPATH) at $DEVNAME.
    /opt/bin/k810_conf -d $DEVNAME -f on
fi

Also, one little thing: You can use udevadm info -a -n /dev/hidraw1 to get the right address instead of hcitool (replace with the right hidraw). It should match, but just to double check (that's how I figured udev is seeing a lower case address).