Subwoofers - Grille off or on?

Wrong. It depends on the baffle design. Many speakers will definitely sound better with the grill on.

A grill on or off is irrelevant for a subwoofer and makes no difference.

We find it easy to hear cloth soften the attack of a kick-drum and reduce the percussiveness of a string bass. It is best described as hearing a 'mumble' or a 'stumble' in the 50-70Hz range.

Huh? The "attack" on a kick drum is around 5 KHz. Most sound engineers can confirm this for you. How this can affect a subwoofer would be a mystery unless it were run full range like a bass guitar amp/speaker.

The main issue (apart from some very slight attenuation in higher frequencies) with grills is the way the baffle is designed. Some baffles have very sharp corners and the grill acts to help reduce the severity of this baffle step and edge diffraction.

I would add that the baffle step is usually somewhere around 400 to 800 Hz and edge diffraction is something that affects imaging mostly in the midrange and treble. Neither of these frequencies are terribly important for a high quality subwoofer that should not output high amounts of harmonic distortion.