I feel your pain. My son was a happy spitter too... I put so much damn milk into that kid, just to keep some of it in him. SO frustrating. So you don't say if you are breast or formula feeding, so I'll just tell you what I did. My ds was about 85% breast fed (both breast and bottle) and about 15% formula fed. In any bottle he got (breastmilk or formula) we added rice cereal, starting at about 15 weeks. My pediatricians are all lactation consultants too, and this was a their recommendation. And I tried to make sure that the bottles he got were from 4 pm and after (I stayed home 5 days a week, worked 2.) So on the days I was home, anything he got after 4 pm was in a bottle with rice. I also started solids right at 4 months. Now, that's earlier than they recommend now, but again, with the heavy spitters, I think you have to make your own decisions. The trick with the solids is that they have a lot fewer calories than breastmilk/formula, but they stay down better. I think it might be a wash in the end, but I often tried to mix some breastmilk or formula powder into whatever he was eating to up the calories a little bit... I would run all this by your pediatrician, but that's what we did.
Now for the sleep thing: You have to get some. My husband and I traded off nights in the guest room so one of us got some decent sleep at least a couple nights a week. If you are a single mom, then, well you are screwed on that front, but if there is another adult in the house then start using him or her. If the baby gets some formula, the world won't end. Either trade nights (what we did) or trade times (he gets up until 2, you get up after 2, or whatever). Personally, I think trading nights works best because if I hear the baby, I'm up. The goal is to survive the next six months... anyway you can get there.