Right, if you want this to stop you are in complete control here.
And as someone who is a single mother with their own home let me tell you to stop thinking about that magical family unit. You have the absolute holy fucking grail, you have a child, you have financial independence, you have a stable roof over yours and your childs head, you can live life exactly as you please.
The bloke - you bag all of his stuff off and drop it back at his parents or put it by the front door if you don't drive. You tell him that the situation had got carried away and you are not happy with it and he is to move back to his parents there and then. It's not up for discussion, you are an adult and in control, you don't want to be in a relationship with him and you are going to focus on you and the baby. He can see the baby A, B, C nights from x - Y time and can read him a story over facetime 6pm every other night or whatever suits you
Help with the baby - if you don't have family help you can buy it in and it'll be much cheaper than carrying this cocklodger, mothers help, au pair, nanny, babysitters, child minders, nurserys, Home start volunteers there is a whole industry of childcare out thereto find what works for your situation.