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Not an expert on all options especially on that child support negative but:
5000/12 = 4166 / month gross income.
You're going to have some minimum payments which might matter on those credit cards, sloppy math calling them $50 each for the two outstanding revolvers: $100 + 359 + 455 + 209 = 1123.
DTI FE Ratio = 27.0%
Handwaving 150k mortgage 15k down (gift maximum) 4.5% is something like 850 in total payments.
DTI BE Ratio = 47.4%; might be a bit high for conventional, gets worse at 200k, and if your listed credit report minimum payments are higher that's going to factor too. Also missing closing costs in there. Personally that seems a little tight to me though others have done it, but I'd really look hard at it TBH.