Basically, there is very little way to do this without involving a gunsmith who works with NFA items. Yes, for those few minutes of having the FH off, if the barrel is still on there/able to fire, it's an SBR. Annoying, no? :barf:
In any case, it's worth getting the SBR stamp in addition to the silencer. It's a great little SBR, it cries out for you to do it.