Silent Reflux and Sleep Positions

So my girl is 4 weeks and has silent reflux (reflux but doesn't vomit/spit up huge ammounts, it usually just goes up her esophagus/back of throat). Anytime she lays down after eating I can hear her gurgling/coughing/choking on it and then she usually starts crying from the pain. I keep her upright after she eats to prevent this but I used to only have to hold her upright for 30-40 minutes and then she would be okay to lie down but it's getting longer and longer now to the point where even if I lie her down an hour and a half after eating it happens.

I don't know what to do to help her because I hold her upright for so long and by the time I can finally put her down she is hungry again within half an hour so it's become impossible for me to sleep.

I feel like if I put her to sleep on an incline I would not have to hold her up anywhere near as long but I'm terrified of the increased SIDS risk.

Does anyone have any suggestions/advice?