Last night I tried this:

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When I put the cap on the first time, my initial thought was that the mask would probably slip - but it was slipping already, any way, so I'd make adjustments from there. I thought I might have to sew some ties on it and maybe some velcro on the back of my mask. The lace around the crown of the head works well with velcro, by the way.
I used just the mask last night - absolutely NOTHING slipped. I bunned my hair and put the cap on. The cap did not slip at all, either.
I am impressed. This morning I purchased a few more things to try out with my mask at night - I'll update this with each trial as I try each product.
Happy Happy.
PS Ladies, if you've found anything else that works - please be invited to post about it here.