The expenses that do not show up in most cases is payroll because the Tax category in your chart of accounts is "Payroll Expenditure". This is because QuickBooks wants to pull your payroll expenses along with the hours and you will not be able to achieve this unless you use QB payroll which links to your ledger.

The solution is simple. Go to your chart of accounts and for all payroll related GL codes, change the tax form from "Payroll Expenditure" to "General and Admin". Rerun your project costs and you should see the GL codes included in your project cost.