There is a growing misconception that none is always singular. It’s not. It can be singular or plural. However, this “rule” is so well promulgated, many of your grammar-savvy readers will expect it to be singular. If your none translates as not one, treat it as singular. If it better translates as not any, treat it as plural. Your best bet is to play it by ear. Or, try your hardest to treat none as singular, but, if you can’t bear how it sounds, go plural.
I think yours works well with a singular "none", i.e. it means "not one".