I made a similar mistake of adding too much fluid after I thought the smoke unit might have been defective. Upon emailing BLI they said to just do not add any fluid for awhile, and that the fluid sometimes forms a bubble over the stack which inhibits the smoke from coming out. BMI suggested blowing into the stack to eliminate the bubble. Meanwhile, I discovered that by lightly blowing through the smoke box this will excelerate the dissipation of the fluid. My Hudson is now working satisfactorily, although the smoke is not overly generous.
Merely inverting the engine may not be enough. It might help to gently shake the engine, but with a hand wrapped in paper towel held over the smoke unit to readily detect if it is worth doing what you are doing.
However, I do agree that a phone call to BLI to ask for some tips is the way to go...just to cover all the bases.
-Crandell
Methinks you'd be better off e-mailing Broadway Limited on this one.
http://www.broadway-limited.com/customerservice.aspx