Yeah, my previous experience with MYOB under WINE and VirtualBox was subpar. It was a long time ago though so might be worth another go.
As you've obviously experienced the web version is pretty well useless unforuntately. I actually ran MYOB on Windows Server back in the day, and used remote desktop from whatever Linux PC or laptop I was using at the time. Then it stopped working with Windows Server so there went that loophole. Also I was using an out of date version of Windows Server just to maintain MYOB functionality which in hindsight seems like a bit of a silly sausage thing to do.