I was looking around the net and here are some good links to some reading material with regards to swallowing issues. They are not specifically to do with PSP, but they look pretty good nevertheless.
This is advice for swallowing after a stroke, but is good advice generally. However ignore the bit where it recommends encouraging self-eating. Unlike stroke victims encouraging self-eating is not recommended, so the person should always receive help when eating from the caregiver.
This is a video of the chin tuck technique, but I never really tried it so do not know if it is any good. Furthermore, I think this technique is rather limited once the neck becomes more stiff and rigid.
We were advised to lean the person forward when swallowing and also to let the person swallow at least a couple of times between each spoonful. We also used Thick n' Easy powder to thicken drinks and used Ensure Creme chocolate puddings which were very good. I eventually gave up leaning the person forward when eating but ensuring the person swallowed multiple times between each spoonful worked well. Ensuring the person is in an upright posture is also important. I only recently learned that someone should not lie down at least 30 minutes after eating too. Furthermore, the neck later on can become very stiff and rigid, thus again perhaps exacerbating the swallowing difficulties. Evetually there may be hyperextension of the neck and some sort of neck support may be required. I know I suggested a couple of weeks ago lifting the back of the head up when swallowing, and while it helps with swallowing I would be careful doing this because the neck is a very sensitive area and I am not sure how safe it is. I think the best initial strategy may be to prop up the back of the head and neck with pillows when eating. Additionally, for the neck issue simply massaging the neck muscles a bit and using a small amount of painkiller may help too. I thought I saw some improvements in swallowing after using a small amount of painkiller and I think it might have been because it helps to reduce some tension and pain in the neck, as well as reduce any pain in the mouth. The baby oral suspension painkillers you get in the shops mixed with some dessert may be the easiest to swallow. Although you have to be careful because even these baby oral suspension painkillers can be difficult to swallow and can cause gagging, thus why they should be mixed with something. Muscle relaxants are supposed to be good for tension and pain in the neck too. Lastly, cotton buds dipped in mouth wash are good for keeping the insides of the mouth clean too.