An alternative would be to make your own surface primer, by using your preferred clear coat, or white or light grey paint, and stir in some talcum powder, until you have a "heavy" but fluid "goo" - I call this porridge, and use it for this kind of problem, and filling very narrow joints etc.
Note that this works best with enamel paint / varnish, is still fairly good with acrylics, but does not work very well if using Johnson's Klear/Future.
Apply a generous layer over the affected area, using a paint brush, and allow to fully harden, preferably for at least 12 hours. Once hard, it can be sanded easily, and any "pin holes" can be filled with a further coat if needed.
This is a "traditional" technique used to fill the grain on balsa wood, and I've used it for over fifty years when making balsa masters to mould clear canopies or other styrene parts ( the master is given a number of gloss clear coats to finish, in order to present a glass-smooth surface).
Hope this helps.