I think we need more information from your tax return to figure this out: AGI, taxable income, withholding, tax due, and credits.
Changing from single to HOH should reduce taxes owed ($6k+ extra deduction), and CTC is an extra $2k tax credit...
If GF's income is low, it might make sense for her to claim the child, if eligible for EITC. You'd have to run both of your returns both ways to see what nets the largest combined refunds for you 2 as a couple. We do this with the kids and the decision on who claims college expenses - usually ends up best for us to put taxable scholarships on the kid's return as taxable income, then we get a higher AOTC credit (which the child can't claim, even the refundable part). We pay the additional tax the child owes, on their behalf.