Grid stoppers are never a problem, and always good practice. They are usually more important with tubes that have higher transconductance - the 12AU7 is nominally 2200 micromhos, vs. 5500 for a 2A3 or a 12AT7. Though very similar, the Foreplay III is the first one that I designed, and I always use stoppers.
For noise and microphonic problems, you may want to adjust teh gain budget of your system. See the notes on signal and noise levels on the Community page, if you have not already.