I've worked for this team before as a Lead Software Developer (I was an hourly contractor then as well) and I did indeed lead a team of other developers. They were thrilled with me, the pay was good so I worked my butt off for them.
This was circa 2017. So the question is, how much would I charge today with more experience and the better job title?
I don't really feel comfortable disclosing hourly rate, so if you could just use example numbers or as a percentage I'd appreciate it.
The only thing that I know for certain is I'm not charging less!
I'd say take your 2017 hourly rate and double it. If they act all hurt on that number, then they should hire you FT with benefits.