Unless you measured him before and after every single feeding - then your assessment of not producing enough is false. Please don't sell your wonderful body's design short. You ARE producing enough, but due to supplemental feedings, you are telling your body to produce LESS because your son isn't suckling each and every time he needs to feed. His constant suckling is what will tell your body to increase the production.
Formula has foreign proteins, foreign bacteria (which is why formula can cause either extreme of diarrhea or constipation) and causes inflammation and irritation of the baby's immature digestive tract. I would counsel you to stop all formula and start breastfeeding on demand. If it's every 20 minutes, then do so until your body can get back to what it should be (usually takes less than 48 hours of on demand nursing) in milk production. Soy should be a last resort, especially for boys. Between the increase of hormone imbalance from the soy (much like estrogen) and the GMO soybean used in the mainstream brands - I don't think that will be helpful. Breastfeeding exclusively will immediately cut down spending on expensive formula and give you extra money to put elsewhere where it's most needed.
For the pooping... breastfed babies can poop up to a few times a day or once a week. Breastmilk is so easily absorbed by the body that the waste is minimal (hence not as much poop and not as often). Formula fed infants tend to have 3-4 poops a day because most of what they consume is waste - and what they DO poop is usually very yucky smelling (like adult poop). This usually can cause an issue in young infants if both formula and breastfeeding. Should be one or the other consistently for the first 4-6 months.
For gas... babies are gassy. Their bodies are brand new and it takes about 3-4 months for their body to mature most of the way into being more what we know as normal. Their GI system doesn't mature until 7-8 months, swallowing ability doesn't occur until 6-7 months and their sphincter which closes off the stomach from the esophagus takes about 4-5 months to mature (when spitting up is less of an issue). These things are normal. Gripe water really worked well for my little one, who is 5 weeks now, 6 weeks on Monday. I will also stagger with baby Gas drops. He is exclusively breastfed from day 9 because the first 9 days he was force fed formula and breastmilk thru a nasal tube.
My son is gassy no matter what I eat. I don't eat much dairy anyways except for frozen yogurt and organic yogurt, with the small bit of organic milk in my cereal - - but the normal 'gassy' foods like eggs, broccoli, etc I eat in moderation to help with the gas - but I don't see a difference one way or the other. The burping often, lots of tummy time, bicycling and pumping his legs, as well as the gripe water/gas drops seem to make him feel fine. He IS colicky, but if that's his only issue - I'm happy... many other children have some major issues now a days.
Please try to gain some support and real life experience from Le Leche League Moms - they have meetings all over the country and I'm sure there is a nearby chapter for you. They can help ease your fears and give you the help from a real person - which it sounds like you really need.