I completely understand. My daughter was diagnosed with a primary sleep disorder at birth, and a pediatric neurologist (and team of doctors) agreed that her brain really didn't know how to sleep. I nearly lost my mind. She didn't sleep during the day, either (less than 2 hours out of 24). We tried swaddling, diet changes, sleep training, etc, and eventually resorted to some medication with the specialist's supervision to help her learn to sleep. She had her first sleep study at 5 months of age. She was in significant distress too.
We found out that she was severely intolerant to baby apple juice. Apple juice contains sorbitol (naturally) and it can cause many digestive issues. Are you giving your baby any juice at night in a bottle, for example? Are you eating or drinking anything that's "diet" or artificially sweetened? Our baby's GI specialist told us that she advised many of her patients' mothers to cut all that stuff out if the baby was gassy or constipated or had other digestive issues. Also, are you taking vitamins or supplements?
Since your baby sleeps during the day, you know he's capable of sleeping. So what's different about the night time? Ask your doctor why the gas upsets him at night, but not in the daytime naps. Does he nap during the day and (try to) sleep during the night in the same cradle, or crib, or room? What is the daytime environment (noise, activity) vs night time environment (is it to too quiet, too warm, etc)? Have you tried gas drops? Have you asked a pediatric GI specialist about his gas? Have you taken a video of his distress at night and kept a food log? Maybe there's something you're only eating at night that distresses him. Start keeping a log of his nap times, nighttime sleep efforts, feeding times, your diet, etc. I'm just throwing ideas out there, from someone who's had to do all these things.
The most important thing, if you get a night sitter, is to not have someone keep him entertained at night, or play with him, or just soothe him to keep him quiet. The night sitter should focus on following sound techniques to help the baby learn to sleep. The ultimate goal is a baby/toddler/child who sleeps at night and plays/learns/goes to school during the day (at appropriate ages and with appropriate naps). You may need to consult a pediatric specialist who understands babies with sleep difficulties, and come up with a plan to train the baby, and then make sure that the night sitter follows that plan to the letter. If the night sitter walks around all night bouncing the baby so the baby doesn't cry, that will certainly provide you with some sleep time, and provide your family with some quiet, but it won't help the baby in the long run.
I ended up hiring a young pre-teen, not for night time, but for my other child (my son had just turned 4 when the baby was born), after school or late afternoons. I would make sure the baby was securely and safely in her crib, and sure enough, she'd cry, but for a blessed few minutes, the pre-teen was playing happily with my son (building with blocks, racing his trucks and cars), helping him get a snack (helping him make a peanut butter sandwich, or supervising a treat of graham crackers and milk - no cooking), and I'd grab a nap, a shower, make dinner, whatever. I didn't need an experienced older teen as I was right there in the house, but I needed to know my son was entertained and the baby was safe, and I could take some time for myself. I made sure the girl I hired understood that it would be noisy (with a crying baby) and her mom prepared her well. She did a great job helping me out during the afternoons and early evenings. It helped keep me sane during those very long nights.