I been here since April 2016 Sirius.
Oh that's a shame. That overstay will affect when you can be granted British citizenship.
Did you know that your partner can do more than one job to meet the financial requirement to sponsor? With the minimum wage rising to £7.50 for the age 25s and over this week, that is just under 48 hours a week if all he can only get is minimum wage. He would need to continue both those jobs until your partner/spouse visa is in hand.
Whatever you decide; to try to get the 10 years and four visas and four lots of the IHS to ILR by trying to use your British child, or to return to the UK on a partner visa, (or marry for a spouse visa) for 5 years to ILR; he should still sort out his Tax Credits claim. See what they say about you being there for a year and his single parent claim as I don't know how they will view that. UKVI shares information with HMRC and it is much better if he approaches HMRC (Tax Credits) before they approach him.
Get some health insurance too as the NHS can add 50% to the bill if there is no insurance. If you try for that 10 year route, it won't be a quick answer.