Hi Panamajack..You said the white dots 'seem' to be propagating? Did you mean multiplying?
Are you familiar with Mealy Bugs? They're fuzzy, white/gray patches..
They can be wiped off with paper or cotton balls.

First you need to make a definate ID. Be it mold or mealy.
Another First is ISOLATE from other plants..Mealy will spread on other plants...these bugs are plant killers.
Mealy can be scraped off..The difference between ID'ing mealy and mold is, mold usually grows near soil..you can find mealy on and under a leaf, stems, trunk. They're inclined to hide.
W/your pineapple, (like other Bromiliads) that have urn-like tops, mealy makes a home inside the urn among foliage. Look inside the upper leaves, too.

If it is mealy, and your pineapple isn't infested to the point the plant should be discarded, wipe off spots with Rubbing Alcohol. You can use small pieces of cotton balls or Q-tips.
Please keep us posted..Toni