A few things that helped me when we were here:

Switch to goat milk rather than cow.
Porrige before bedtime will fill up the tummy and stop him feeding so much at night.
Is a dummy worth trying if he just needs to suck while he sleeps?
If you're not comfortable with feeding so much, can you offer fruit/flapjack/vegetables or whatever food you think best?

Liebling dropped his day sleeps at about 16m and sometimes only needed 3 hours overnight. If you can roll with it, teach him to play quietly while you sleep on the sofa. Curl up on the sofa/in bed with his favourite film and sleep as he watches. And who cares about "children shouldn't watch TV" - children also should sleep and let their mothers sleep. If that isn't happening, you need some survival skills.

Don't pin your hopes on the allergy appointment - the one we had asked me which allergies Liebling had, when I said that's what I was here to find out they said they'd only test for what I said he was allergic to. Which, to my mind, was stupid: I don't know what the problem is. And they don't test for intolerances, only allergies.