If you can't get any better advice and feel desperate you could try the following configuration change that may allow your operating system to detect the touch screen differently and add the correct driver (or at least it may offer some different clues to help a step forward):
But please note that if you try this config change there is a high likelihood that your touchpad or mouse will stop working (but if I understand correctly you are not relying a touchpad or mouse anyway...). If this happens you will have to hard power off (hold power button 10 seconds).
Anyway here is the config change:
Open the file /etc/X11/xorg.conf
Have a look at the section labelled:
#*******************************************
#Server flags section
#******************************************
You will probably see the following option:
Option "AutoAddDevices" "false"
Change this to:
Option "AutoAddDevices" "true"
Then save the file.
Now use the main menu to reboot.
Hopefully after the (soft) reboot the system will now detect the touchscreen more appropriately and load the correct driver module (or at least one of the other similar touchscreen drivers) instead of the generic "mouse" driver which is not calibratable.
If possible run lsmod again and see if there are different modules loaded.
Depending on which Puppy you try this config change on you may see the eGalax driver loaded - or instead there may be other drivers (such as evdev or similar) that interface the touchscreen. If eGalax loads then the xinput calibrator (or the TK cli version i posted about) may now help with calibration. Try various Puppies (including older ones like Lupu) with this technique and see what happens.