Couple of Questions about Diet- and throwing up

I have two health questions. I am new to this site and love it! I hope that my questions arent redundant.

The first is- I have 3 cats who I love- (I took them to New York with me and we live with my husband in a NYC studio)
Well, Raven needs to go on a diet. We are at work all day and sometime have to leave them for the weekend. So we have auto feeder that we have used since they were babies. They are used to getting food when they want it. So- how do I start training them to eat when I want them to eat and control their portions. Any advice will be helpful!!

I also saw the post about the kitten who throws up... my 4 year old kitty Leif throws up all the time. His story is- he was rejected by his mother as a baby. He was found with broken back legs because a log pile fell on him. (My sister found him) My sister fed him herself as a baby. He has been through so many of his 9 lives already...including being bit by a dog, whiskers burnt off, and the list goes on. He doesn't have much luck.

Anyway, back to the throwing up. I look him to a great vet who was recommended by many cat people. The vet looked at him and really didn't help. She said it might be hairballs. Which I know already ITS NOT! He binge eats. He eats really fast and then throws up. I see it with his dry food- he doesn't even chew- he swallows his food whole! There is nothing wrong with his teeth (We play all the time).

What else should I do?

I would transition them to less dry food - load their auto feeder with what they should have between the 3 of them for a 24 hour period (based on the feeding guidelines on your brand's of cat food's package, and based on their current weight range), and supplement at the end of the day (in case they have gone through all of it) with a meaured amount of a quality canned food (adjust the amt. of dry to allow for the addition of wet, as you don't wish them to gain weight).

Seperate issue - the eating so quickly and then vomitting can be helped by elevating his food dish. That I realize is an issue if you are using an autofeeder - any chance you can place it securely on a step stool or low wooden footstool so it is elevated?