Is the refinance amount mortgage plus $ to H or just mortgage? If the former, and he isn’t aware as yet child support is being factored into your borrowing capacity, then ascertain max borrowing capacity you have without CS being factored in (ie just on your income) and tell him you’ll pay him whatever it is you can borrow above the mortgage amount because that’s your capacity.
Or, tell him what you’ve posted in the update email but add if he does a binding cs agreement you won’t have to wait 6 months (provided a bcsa is valid income for the lender per my previous postings). A bcsa will cost a few grand though.
Or, include a clause in the consent order that rather than refinance the mortgage into your name you’ll be responsible for mortgage repayments and indemnify him pending refinance in 6 12. 18 whatever months time.
If none of the above suits you, then your email sounds ok but I’d drop the inconvenience part at the end. Maybe drop the current income bit too as that may prompt him to hound you to get a better paying job
Cheers DS
Me: early 40's XW: nearly 50 T: 15 M: 5 BD: Jan 19 S:10 SS: 22 SD: 24
