I use Quickbooks as bookkeeper for my husband's business, and I get the budgeting thing. (We have payroll and some other things that will make me stick with QB.) I recently started a YNAB file for the business and even though it means entering the same info twice, it's a snap thanks to autofill.
I don't have the advice you want because I don't know the answers. I just wanted to say that at first I was very reluctant to "waste my time" budgeting for categories that get paid out based on what money we get in. There's no point budgeting for materials or payroll, for instance, because they are what they are and as soon as the customer pays us, we turn around and pay the materials and payroll (and subs, etc.).
However, as you say, YNAB allows me to see very clearly WHAT'S LEFT. And that was the piece that has always been missing. Now when we get paid and payroll and materials are paid for, I zero out those categories. While in your personal life you wouldn't want to let those categories go negative, in this situation it's OK because we know for sure that the income will cover those expenses. Unlike with a personal paycheck, this income is tied directly to those expenses, line by line.
Then I take what's still available to budget and divide it into the truly budgetable categories, like worker's comp and liability insurance, and a nice healthy "buffer" category (not in the YNAB sense; in the sense that if there's a slow week we still can pay the month's bills). This has turned everything around. Now I am always sure there's enough money to pay for taxes and insurance and I don't get the idea that because the account balance is fat that we can spend more than we can afford.
I do wish there were a hybrid that allowed QB to work with YNAB, but honestly it would only save me about 10 minutes a week, if that, in copying entries from QB to YNAB. Totally worth it.
Projected debt-free date as of Aug. 25, 2012: November 2015
Projected debt-free date as of Sept. 2, 2012: August 2015
Projected debt-free date as of Sept. 20, 2012: March 2015
Projected debt-free date as of Feb. 13, 2013: October 2014