I think its about time I throw away the hair dryer and go for a more sophisticated solution to dew.
What do people recommend for a 12" (f4) astrograph?
1. A controller with 3-4 outputs?
2. Strap for the tube
3. heater for the secondary? (is this necessary?)
4. heater for the eyepiece (eg if I use a barlow)?
I'd say yes to all of the above, it doesn't take long or much for dew to start working its way into places you don't want it. The focuser is high up towards the top and I have had dew start forming on the secondary and towards to focuser within an hour of setup on a bad night.
Yes to the secondary heater and eyepiece heater. You don't really need a strap for the tube, the primary is way down there shielded from the sky, and I have never had a primary dew up.
Kendrick controllers and heater bands are about the best around. The DigiFire 8 is a new model that's just been released and is perfect for a dob. Kendrick sell a range of secondary heaters to suit your secondary setup. I also use the Dewminator eyepiece heater because it works well with the biggest eyepieces.
I stumbled across R Sky http://r-sky.org/en/products they seem pretty well priced and the secondary heater looks super easy to install. not sure how my gso spider vanes would go, they are soooooo soft.
I agree with Allan - go Kendrick: robust, excellent quality kit.
The only issue I have is when observing using only battery power those dew straps can be thirsty electron guzzlers unless you have hem running just above ambient (which is all you need).
Sometimes prevention is the best cure.
Have you tried attaching a foam disk, same diameter as the secondary, on top of the spider vanes, with a very shiny metalized surface facing the sky. It works wonders on my 16" Dall-Kirkham. Although you may also need a heater for the focuser area.