OP, just find someone who wants to work with you…but on a trial basis for a month or two. You can both be self-employed, but you control where you buy stuff, looking at jobs, pricing etc. For year one, you split profits 60-40, then 55-45 year two, then 50-50. Each time the split works more for him/her, he/she has to take more responsibility.
If your work is mainly domestic, you can get every second cheque paid to you. Every month sit down together and work out how the split has worked – then whoever’s behind gets the next cheque. It’s a bit of a faff, but he/she won’t spend every day trying to hang the job out for an extra day’s work either.