Yes it works really well for set ups like this.
On the reddit sub they generally say if you are going to do business expenses, have a business specific budget. You can have I think unlimited budgets and swap between them as much as you want. You can even have two budgets open in different tabs.
So I think I'd have your main budget which is joint, current, loan, DH's 2x accounts.
And then a separate business budget with just the business account.
If you make payments from the business account to one of your accounts, it's just an outflow to <name> on the business budget, or an inflow on your main budget from <business> and vice versa.
I don't have specific categories for different accounts. I think you'd get tied up in knots trying to do that. Keep them separate.